Articles de revues : « Generalized nilpotence »

1

Kalogeropoulos. « NILPOTENCE AND THE GENERALIZED UNCERTAINTY PRINCIPLE (S) ». American Journal of Space Science 1, n^o 2 (1 février 2013) : 99–111. http://dx.doi.org/10.3844/ajssp.2013.99.111.

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Kalogeropoulos, Nikolaos. « Nilpotence in physics : Generalized uncertainty principles and Tsallis entropy ». Qatar Foundation Annual Research Forum Proceedings, n^o 2012 (octobre 2012) : EEP19. http://dx.doi.org/10.5339/qfarf.2012.eep19.

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Asaad, Mohamed. « On weakly ℌ-embedded subgroups and p-nilpotence of finite groups ». Studia Scientiarum Mathematicarum Hungarica 56, n^o 2 (juin 2019) : 233–40. http://dx.doi.org/10.1556/012.2019.56.2.1374.

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Abstract Let G be a finite group and H a subgroup of G. We say that H is an ℌ-subgroup of G if NG (H) ∩ Hg ≤ H for all g ∈G; H is called weakly ℌ-embedded in G if G has a normal subgroup K such that HG = HK and H ∩ K is an ℌ-subgroup of G, where HG is the normal clousre of H in G, i. e., HG = 〈Hg|g ∈ G〉. In this paper, we study the p-nilpotence of a group G under the assumption that every subgroup of order d of a Sylow p-subgroup P of G with 1 < d < |P| is weakly ℌ-embedded in G. Many known results related to p-nilpotence of a group G are generalized.

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MELIKHOV, SERGEY A., et DUŠAN REPOVŠ. « n-QUASI-ISOTOPY I : QUESTIONS OF NILPOTENCE ». Journal of Knot Theory and Its Ramifications 14, n^o 05 (août 2005) : 571–602. http://dx.doi.org/10.1142/s0218216505003968.

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It is well-known that no knot can be cancelled in a connected sum with another knot, whereas every link can be cancelled up to link homotopy in a (componentwise) connected sum with another link. In this paper we address the question whether the noncancellation property of knots holds for (piecewise-linear) links up to some stronger analogue of link homotopy, which still does not distinguish between sufficiently close C0-approximations of a topological link. We introduce a sequence of such increasingly stronger equivalence relations under the name of k-quasi-isotopy, k∈ℕ; all of them are weaker than isotopy (in the sense of Milnor). We prove that every link can be cancelled up to peripheral structure preserving isomorphism of any quotient of the fundamental group, functorially invariant under k-quasi-isotopy; functoriality means that the isomorphism between the quotients for links related by any allowable crossing change fits in the commutative diagram with the fundamental group of the complement to the intermediate singular link. The proof invokes Baer's theorem on the join of subnormal locally nilpotent subgroups. On the other hand, the integral generalized ( lk ≠ 0) Sato–Levine invariant [Formula: see text] is invariant under 1-quasi-isotopy, but is not determined by any quotient of the fundamental group (endowed with the peripheral structure), functorially invariant under 1-quasi-isotopy — in contrast to Waldhausen's theorem.As a byproduct, we use [Formula: see text] to determine the image of the Kirk–Koschorke invariant [Formula: see text] of fibered link maps.

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Kelarev, A. V., et J. Okniński. « On group graded rings satisfying polynomial identities ». Glasgow Mathematical Journal 37, n^o 2 (mai 1995) : 205–10. http://dx.doi.org/10.1017/s0017089500031104.

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A number of classical theorems of ring theory deal with nilness and nilpotency of the Jacobson radical of various ring constructions (see [10], [18]). Several interesting results of this sort have appeared in the literature recently. In particular, it was proved in [1] that the Jacobson radical of every finitely generated PI-ring is nilpotent. For every commutative semigroup ring RS, it was shown in [11] that if J(R) is nil then J(RS) is nil. This result was generalized to all semigroup algebras satisfying polynomial identities in [15] (see [16, Chapter 21]). Further, it was proved in [12] that, for every normal band B, if J(R) is nilpotent, then J(RB) is nilpotent. A similar result for special band-graded rings was established in [13, Section 6]. Analogous theorems concerning nilpotency and local nilpotency were proved in [2] for rings graded by finite and locally finite semigroups.

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Camina, Rachel D., Ainhoa Iñiguez et Anitha Thillaisundaram. « Word problems for finite nilpotent groups ». Archiv der Mathematik 115, n^o 6 (17 juillet 2020) : 599–609. http://dx.doi.org/10.1007/s00013-020-01504-w.

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AbstractLet w be a word in k variables. For a finite nilpotent group G, a conjecture of Amit states that $$N_w(1)\ge |G|^{k-1}$$ N w ( 1 ) ≥ | G | k - 1 , where for $$g\in G$$ g ∈ G , the quantity $$N_w(g)$$ N w ( g ) is the number of k-tuples $$(g_1,\ldots ,g_k)\in G^{(k)}$$ ( g 1 , … , g k ) ∈ G ( k ) such that $$w(g_1,\ldots ,g_k)={g}$$ w ( g 1 , … , g k ) = g . Currently, this conjecture is known to be true for groups of nilpotency class 2. Here we consider a generalized version of Amit’s conjecture, which states that $$N_w(g)\ge |G|^{k-1}$$ N w ( g ) ≥ | G | k - 1 for g a w-value in G, and prove that $$N_w(g)\ge |G|^{k-2}$$ N w ( g ) ≥ | G | k - 2 for finite groups G of odd order and nilpotency class 2. If w is a word in two variables, we further show that the generalized Amit conjecture holds for finite groups G of nilpotency class 2. In addition, we use character theory techniques to confirm the generalized Amit conjecture for finite p-groups (p a prime) with two distinct irreducible character degrees and a particular family of words. Finally, we discuss the related group properties of being rational and chiral, and show that every finite group of nilpotency class 2 is rational.

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Han, Maoan, et Valery G. Romanovski. « Limit Cycle Bifurcations from a Nilpotent Focus or Center of Planar Systems ». Abstract and Applied Analysis 2012 (2012) : 1–28. http://dx.doi.org/10.1155/2012/720830.

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We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds of the maximal number of limit cycles bifurcating from the nilpotent focus or center. The main results generalize the classical Hopf bifurcation theory and establish the new bifurcation theory for the nilpotent case.

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Chauhan, B., S. Kumar et R. P. Malik. « Nilpotent charges in an interacting gauge theory and an 𝒩 = 2 SUSY quantum mechanical model : (Anti-)chiral superfield approach ». International Journal of Modern Physics A 34, n^o 24 (29 août 2019) : 1950131. http://dx.doi.org/10.1142/s0217751x19501318.

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We exploit the power and potential of the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism to derive the nilpotent (anti-)BRST symmetry transformations for any arbitrary [Formula: see text]-dimensional interacting non-Abelian 1-form gauge theory where there is an [Formula: see text] gauge invariant coupling between the gauge field and the Dirac fields. We derive the conserved and nilpotent (anti-)BRST charges and establish their nilpotency and absolute anticommutativity properties within the framework of ACSA to BRST formalism. The clinching proof of the absolute anticommutativity property of the conserved and nilpotent (anti-)BRST charges is a novel result in view of the fact that we consider, in our endeavor, only the (anti-)chiral super expansions of the superfields that are defined on the [Formula: see text]-dimensional super-submanifolds of the general [Formula: see text]-dimensional supermanifold on which our [Formula: see text]-dimensional ordinary interacting non-Abelian 1-form gauge theory is generalized. To corroborate the novelty of the above result, we apply the ACSA to an [Formula: see text] supersymmetric (SUSY) quantum mechanical (QM) model of a harmonic oscillator and show that the nilpotent and conserved [Formula: see text] supercharges of this system do not absolutely anticommute.

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Chauhan, B., S. Kumar et R. P. Malik. « (Anti-)chiral superfield approach to interacting Abelian 1-form gauge theories : Nilpotent and absolutely anticommuting charges ». International Journal of Modern Physics A 33, n^o 04 (10 février 2018) : 1850026. http://dx.doi.org/10.1142/s0217751x18500264.

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We derive the off-shell nilpotent (fermionic) (anti-)BRST symmetry transformations by exploiting the (anti-)chiral superfield approach (ACSA) to Becchi–Rouet–Stora–Tyutin (BRST) formalism for the interacting Abelian 1-form gauge theories where there is a coupling between the U(1) Abelian 1-form gauge field and Dirac as well as complex scalar fields. We exploit the (anti-)BRST invariant restrictions on the (anti-)chiral superfields to derive the fermionic symmetries of our present D-dimensional Abelian 1-form gauge theories. The novel observation of our present investigation is the derivation of the absolute anticommutativity of the nilpotent (anti-)BRST charges despite the fact that our ordinary D-dimensional theories are generalized onto the (D,[Formula: see text]1)-dimensional (anti-) chiral super-submanifolds (of the general (D,[Formula: see text]2)-dimensional supermanifold) where only the (anti-)chiral super expansions of the (anti-)chiral superfields have been taken into account. We also discuss the nilpotency of the (anti-)BRST charges and (anti-)BRST invariance of the Lagrangian densities of our present theories within the framework of ACSA to BRST formalism.

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Krishna, S., A. Shukla et R. P. Malik. « Supervariable approach to nilpotent symmetries of a couple of N = 2 supersymmetric quantum mechanical models ». Canadian Journal of Physics 92, n^o 12 (décembre 2014) : 1623–31. http://dx.doi.org/10.1139/cjp-2014-0047.

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We derive the on-shell as well as off-shell nilpotent supersymmetric (SUSY) symmetry transformations for the [Formula: see text] = 2 SUSY quantum mechanical model of a (0 + 1)-dimensional (1D) free SUSY particle by exploiting the SUSY-invariant restrictions on the (anti-)chiral supervariables of the SUSY theory that is defined on a (1, 2)-dimensional supermanifold (parametrized by a bosonic variable t and a pair of Grassmannian variables θ and [Formula: see text] with [Formula: see text]). Within the framework of our novel approach, we express the Lagrangian and conserved SUSY charges in terms of the (anti-)chiral supervariables to demonstrate the SUSY invariance of the Lagrangian as well as the nilpotency of the SUSY conserved charges in a simple manner. Our approach has the potential to be generalized to the description of other [Formula: see text] = 2 SUSY quantum mechanical systems with physically interesting potential functions. To corroborate the preceding assertion, we apply our method to derive the [Formula: see text] = 2 continuous and nilpotent SUSY transformations for one of the simplest interacting SUSY systems of a 1D harmonic oscillator.

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Jedlička, Přemysl, Agata Pilitowska et Anna Zamojska-Dzienio. « Distributive biracks and solutions of the Yang–Baxter equation ». International Journal of Algebra and Computation 30, n^o 03 (21 janvier 2020) : 667–83. http://dx.doi.org/10.1142/s0218196720500150.

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We investigate a class of non-involutive solutions of the Yang–Baxter equation which generalize derived (self-distributive) solutions. In particular, we study generalized multipermutation solutions in this class. We show that the Yang–Baxter (permutation) groups of such solutions are nilpotent. We formulate the results in the language of biracks which allows us to apply universal algebra tools.

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12

Martindale, W. S., et C. Robert Miers. « Nilpotency and generalized Lie ideals ». Journal of Algebra 127, n^o 1 (novembre 1989) : 244–54. http://dx.doi.org/10.1016/0021-8693(89)90287-1.

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13

Bell, Howard E., et Adil Yaqub. « Generalized periodic rings ». International Journal of Mathematics and Mathematical Sciences 19, n^o 1 (1996) : 87–92. http://dx.doi.org/10.1155/s0161171296000130.

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LetRbe a ring, and letNandCdenote the set of nilpotents and the center ofR, respectively.Ris called generalized periodic if for everyx∈R\(N⋃C), there exist distinct positive integersm,nof opposite parity such thatxn−xm∈N⋂C. We prove that a generalized periodic ring always has the setNof nilpotents forming an ideal inR. We also consider some conditions which imply the commutativity of a generalized periodic ring.

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14

Zhang, Li, Li-Jun Huo et Jia-Bao Liu. « Some New Applications of Weakly H-Embedded Subgroups of Finite Groups ». Mathematics 7, n^o 2 (10 février 2019) : 158. http://dx.doi.org/10.3390/math7020158.

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A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G.

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15

Tan, Yi-Jia. « On nilpotency of generalized fuzzy matrices ». Fuzzy Sets and Systems 161, n^o 16 (août 2010) : 2213–26. http://dx.doi.org/10.1016/j.fss.2010.03.019.

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Riley, David M. « Generalised nilpotence conditions inn-engel lie algebras ». Communications in Algebra 28, n^o 10 (janvier 2000) : 4619–34. http://dx.doi.org/10.1080/00927870008827108.

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Yu, Jie-Tai, H. Bass, E. H. Connell et D. Wright. « On generalized strongly nilpotent matrices ». Linear and Multilinear Algebra 41, n^o 1 (juillet 1996) : 19–22. http://dx.doi.org/10.1080/03081089608818457.

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Bovdi, A. A., et I. I. Khripta. « GENERALIZED LIE NILPOTENT GROUP RINGS ». Mathematics of the USSR-Sbornik 57, n^o 1 (28 février 1987) : 165–69. http://dx.doi.org/10.1070/sm1987v057n01abeh003061.

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Benharrat, Mohammed, et Bekkai Messirdi. « Quasi-nilpotent perturbations of the generalized Kato spectrum ». Georgian Mathematical Journal 25, n^o 3 (1 septembre 2018) : 329–35. http://dx.doi.org/10.1515/gmj-2017-0007.

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AbstractIn this paper, we show that the generalized Kato spectrum of a bounded operator in a Banach space is invariant under perturbation by commuting quasi-nilpotent operators, and the Kato spectrum is stable under additive commuting nilpotent perturbations. Our results are used to give an equivalent definition of the generalized Kato spectrum.

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Paradiso, Fabio. « Generalized Ricci flow on nilpotent Lie groups ». Forum Mathematicum 33, n^o 4 (30 juin 2021) : 997–1014. http://dx.doi.org/10.1515/forum-2020-0171.

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Abstract We define solitons for the generalized Ricci flow on an exact Courant algebroid. We then define a family of flows for left-invariant Dorfman brackets on an exact Courant algebroid over a simply connected nilpotent Lie group, generalizing the bracket flows for nilpotent Lie brackets in a way that might make this new family of flows useful for the study of generalized geometric flows such as the generalized Ricci flow. We provide explicit examples of both constructions on the Heisenberg group. We also discuss solutions to the generalized Ricci flow on the Heisenberg group.

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FRYDRYSZAK, ANDRZEJ M. « NILPOTENT QUANTUM MECHANICS ». International Journal of Modern Physics A 25, n^o 05 (20 février 2010) : 951–83. http://dx.doi.org/10.1142/s0217751x10047786.

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We develop a generalized quantum mechanical formalism based on the nilpotent commuting variables (η-variables). In the nonrelativistic case such formalism provides natural realization of a two-level system (qubit). Using the space of η-wavefunctions, η-Hilbert space and generalized Schrödinger equation we study properties of pure multiqubit systems and also properties of some composed, hybrid models: fermion–qubit, boson–qubit. The fermion–qubit system can be truly supersymmetric, with both SUSY partners having identical spectra. It is a novel feature that SUSY transformations relate here only nilpotent object. The η-eigenfunctions of the Hamiltonian for the qubit–qubit system give the set of Bloch vectors as a natural basis.

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Srinivasan, S. « Finitep′-nilpotent groups. I ». International Journal of Mathematics and Mathematical Sciences 10, n^o 1 (1987) : 135–46. http://dx.doi.org/10.1155/s0161171287000176.

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In this paper we consider finitep′-nilpotent groups which is a generalization of finitep-nilpotent groups. This generalization leads us to consider the various special subgroups such as the Frattini subgroup, Fitting subgroup, and the hypercenter in this generalized setting. The paper also considers the conditions under which product ofp′-nilpotent groups will be ap′-nilpotent group.

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FRYDRYSZAK, ANDRZEJ. « NILPOTENT CLASSICAL MECHANICS ». International Journal of Modern Physics A 22, n^o 14n15 (20 juin 2007) : 2513–33. http://dx.doi.org/10.1142/s0217751x07036749.

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The formalism of nilpotent mechanics is introduced in the Lagrangian and Hamiltonian form. Systems are described using nilpotent, commuting coordinates η. Necessary geometrical notions and elements of generalized differential η-calculus are introduced. The so-called s-geometry, in a special case when it is orthogonally related to a traceless symmetric form, shows some resemblances to the symplectic geometry. As an example of an η-system the nilpotent oscillator is introduced and its supersymmetrization considered. It is shown that the R-symmetry known for the graded superfield oscillator also present here for the supersymmetric η-system. The generalized Poisson bracket for (η, p)-variables satisfies modified Leibniz rule and has nontrivial Jacobiator.

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DE GIOVANNI, FRANCESCO, et MARCO TROMBETTI. « NILPOTENCY IN UNCOUNTABLE GROUPS ». Journal of the Australian Mathematical Society 103, n^o 1 (27 octobre 2016) : 59–69. http://dx.doi.org/10.1017/s1446788716000379.

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The main purpose of this paper is to investigate the behaviour of uncountable groups of cardinality $\aleph$ in which all proper subgroups of cardinality $\aleph$ are nilpotent. It is proved that such a group $G$ is nilpotent, provided that $G$ has no infinite simple homomorphic images and either $\aleph$ has cofinality strictly larger than $\aleph _{0}$ or the generalized continuum hypothesis is assumed to hold. Furthermore, groups whose proper subgroups of large cardinality are soluble are studied in the last part of the paper.

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Jayalakshmi et S. Madhavi Latha. « RIGHT NUCLEUS IN GENERALIZED RIGHT ALTERNATIVE RINGS ». International Journal of Research -GRANTHAALAYAH 3, n^o 1 (31 janvier 2015) : 1–12. http://dx.doi.org/10.29121/granthaalayah.v3.i1.2015.3044.

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Some properties of the right nucleus in generalized right alternative rings have been presented in this paper. In a generalized right alternative ring R which is finitely generated or free of locally nilpotent ideals, the right nucleus Nr equals the center C. Also, if R is prime and Nr ¹ C, then the associator ideal of R is locally nilpotent. Seong Nam [5] studied the properties of the right nucleus in right alternative algebra. He showed that if R is a prime right alternative algebra of char. ≠ 2 and Right nucleus Nr is not equal to the center C, then the associator ideal of R is locally nilpotent. But the problem arises when it come with the study of generalized right alternative ring as the ring dose not absorb the right alternative identity. In this paper we consider our ring to be generalized right alternative ring and try to prove the results of Seong Nam [5]. At the end of this paper we give an example to show that the generalized right alternative ring is not right alternative.

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Robinson, Geoffrey R. « On generalized characters of nilpotent groups ». Journal of Algebra 308, n^o 2 (février 2007) : 822–27. http://dx.doi.org/10.1016/j.jalgebra.2006.04.006.

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Li, Fang. « Characterization of left Artinian algebras through pseudo path algebras ». Journal of the Australian Mathematical Society 83, n^o 3 (décembre 2007) : 385–416. http://dx.doi.org/10.1017/s144678870003799x.

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AbstractIn this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field k when the quotient algebra can be lifted by a radical. Our particular interest is when the dimension of the quotient algebra determined by the nth Hochschild cohomology is less than 2 (for example, when k is finite or char k = 0). Using generalized path algebras, a generalization of Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebra is introduced as a new generalization of path algebras, whose quotient by ken is a generalized path algebra (see Fact 2.6).The main result is that(i) for a left Artinian k–algebra A and r = r(A) the radical of A. if the quotient algebra A/r can be lifted then A ≅ PSEk (Δ, , ρ) with Js ⊂ (ρ) ⊂ J for some s (Theorem 3.2);(ii) If A is a finite dimensional k–algebra with 2-nilpotent radical and the quotient by radical can be lifted, then A ≅ k(Δ, , ρ) with 2 ⊂ (ρ) ⊂ 2 + ∩ ker (Theorem 4.2),where Δ is the quiver of A and ρ is a set of relations.For all the cases we discuss in this paper, we prove the uniqueness of such quivers Δ and the generalized path algebras/pseudo path algebras satisfying the isomorphisms when the ideals generated by the relations are admissible (see Theorem 3.5 and 4.4).

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Abyzov, A. N. « Generalized SV-rings of bounded index of nilpotency ». Russian Mathematics 55, n^o 12 (27 novembre 2011) : 1–10. http://dx.doi.org/10.3103/s1066369x11120012.

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Kurdachenko, L. A., et I. Ya Subbotin. « Pronormality, contranormality and generalized nilpotency in infinite groups ». Publicacions Matemàtiques 47 (1 juillet 2003) : 389–414. http://dx.doi.org/10.5565/publmat_47203_05.

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Arenas, Manuel, et Alicia Labra. « On Nilpotency of Generalized Almost-Jordan Right-Nilalgebras ». Algebra Colloquium 15, n^o 01 (mars 2008) : 69–82. http://dx.doi.org/10.1142/s1005386708000072.

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We study the variety of algebras A over a field of characteristic ≠ 2, 3, 5 satisfying the identities xy=yx and β {((xx)y)x-((yx)x)x} + γ {((xx)x)y-((yx)x)x}=0, where β, γ are scalars. We do not assume power-associativity. We prove that if A admits a non-degenerate trace form, then A is a Jordan algebra. We also prove that if A is finite-dimensional and solvable, then it is nilpotent. We find three conditions, any of which implies that a finite-dimensional right-nilalgebra A is nilpotent.

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Chen, Yizhi, et Xianzhong Zhao. « On Decompositions of Matrices over Distributive Lattices ». Journal of Applied Mathematics 2014 (2014) : 1–10. http://dx.doi.org/10.1155/2014/202075.

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LetLbe a distributive lattice andMn,q(L)(Mn(L), resp.) the semigroup (semiring, resp.) ofn×q(n×n, resp.) matrices overL. In this paper, we show that if there is a subdirect embedding from distributive latticeLto the direct product∏i=1m‍Liof distributive latticesL1,L2, …,Lm, then there will be a corresponding subdirect embedding from the matrix semigroupMn,q(L)(semiringMn(L), resp.) to semigroup∏i=1m‍Mn,q(Li)(semiring∏i=1m‍Mn(Li), resp.). Further, it is proved that a matrix over a distributive lattice can be decomposed into the sum of matrices over some of its special subchains. This generalizes and extends the decomposition theorems of matrices over finite distributive lattices, chain semirings, fuzzy semirings, and so forth. Finally, as some applications, we present a method to calculate the indices and periods of the matrices over a distributive lattice and characterize the structures of idempotent and nilpotent matrices over it. We translate the characterizations of idempotent and nilpotent matrices over a distributive lattice into the corresponding ones of the binary Boolean cases, which also generalize the corresponding structures of idempotent and nilpotent matrices over general Boolean algebras, chain semirings, fuzzy semirings, and so forth.

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Krishna, S., D. Shukla et R. P. Malik. « Novel symmetries in an interacting 𝒩 = 2 supersymmetric quantum mechanical model ». International Journal of Modern Physics A 31, n^o 19 (7 juillet 2016) : 1650113. http://dx.doi.org/10.1142/s0217751x1650113x.

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In this paper, we demonstrate the existence of a set of novel discrete symmetry transformations in the case of an interacting [Formula: see text] supersymmetric quantum mechanical model of a system of an electron moving on a sphere in the background of a magnetic monopole and establish its interpretation in the language of differential geometry. These discrete symmetries are, over and above, the usual three continuous symmetries of the theory which together provide the physical realizations of the de Rham cohomological operators of differential geometry. We derive the nilpotent [Formula: see text] SUSY transformations by exploiting our idea of supervariable approach and provide geometrical meaning to these transformations in the language of Grassmannian translational generators on a [Formula: see text]-dimensional supermanifold on which our [Formula: see text] SUSY quantum mechanical model is generalized. We express the conserved supercharges and the invariance of the Lagrangian in terms of the supervariables (obtained after the imposition of the SUSY invariant restrictions) and provide the geometrical meaning to (i) the nilpotency property of the [Formula: see text] supercharges, and (ii) the SUSY invariance of the Lagrangian of our [Formula: see text] SUSY theory.

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Likouka, Come Chancel. « Nilpotency of the Ordinary Lie-algebra of an n-Lie Algebra ». Journal of Mathematics Research 9, n^o 2 (15 mars 2017) : 79. http://dx.doi.org/10.5539/jmr.v9n2p79.

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In this paper, we generalize to n-Lie algebras a corollary of the well-known Engel's theorem which offers some justification for the terminology "nilpotent" and we construct a nilpotent ordinary Lie algebra from a nilpotent n-Lie algebra.

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Wu, Yusen, Cui Zhang et Changjin Xu. « Limit Cycles and Analytic Centers for a Family of4n-1Degree Systems with Generalized Nilpotent Singularities ». Journal of Function Spaces 2015 (2015) : 1–7. http://dx.doi.org/10.1155/2015/859015.

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With the aid of computer algebra systemMathematica8.0 and by the integral factor method, for a family of generalized nilpotent systems, we first compute the first several quasi-Lyapunov constants, by vanishing them and rigorous proof, and then we get sufficient and necessary conditions under which the systems admit analytic centers at the origin. In addition, we present that seven amplitude limit cycles can be created from the origin. As an example, we give a concrete system with seven limit cycles via parameter perturbations to illustrate our conclusion. An interesting phenomenon is that the exponent parameterncontrols the singular point type of the studied system. The main results generalize and improve the previously known results in Pan.

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Hilton, Peter, et Robert Militello. « On almost finitely generated nilpotent groups ». International Journal of Mathematics and Mathematical Sciences 19, n^o 3 (1996) : 539–44. http://dx.doi.org/10.1155/s0161171296000749.

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A nilpotent groupGis fgp ifGp, is finitely generated (fg) as ap-local group for all primesp; it is fg-like if there exists a nilpotent fg groupHsuch thatGp≃Hpfor all primesp. The fgp nilpotent groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelian groups, a subgroup of an fg-like group is fg-like, and an extension of an fg-like group by an fg-like group is fg-like. These properties persist for nilpotent groups with finite commutator subgroup, but fail in general.

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Dey, Asit, et Madhumangal Pal. « Multi-Fuzzy Complex Nilpotent Matrices ». International Journal of Fuzzy System Applications 5, n^o 4 (octobre 2016) : 52–76. http://dx.doi.org/10.4018/ijfsa.2016100103.

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In this paper, the concept of multi-fuzzy matrix (MFM), multi-fuzzy complex matrix (MFCM), generalized multi-fuzzy complex matrix (GMFCM), generalized multi-fuzzy complex nilpotent matrix (GMFCNM) are introduced and have shown that the set of GMFCMs form a distributive lattice. Some properties and characterizations for GMFCNMs are established and in particular, a necessary and sufficient condition for an n × n GMFCNM to have the nilpotent index n is given. Finally, the reduction of GMFCNMs over a distributive lattice are given with some properties.

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Bell, Howard E., et Adil Yaqub. « On Generalized Periodic-Like Rings ». International Journal of Mathematics and Mathematical Sciences 2007 (2007) : 1–5. http://dx.doi.org/10.1155/2007/29513.

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LetRbe a ring with centerZ, Jacobson radicalJ, and setNof all nilpotent elements. CallRgeneralized periodic-like if for allx∈R∖(N∪J∪Z)there exist positive integersm,nof opposite parity for whichxm−xn∈N∩Z. We identify some basic properties of such rings and prove some results on commutativity.

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Hila, Kostaq, Bijan Davvaz, Krisanthi Naka et Jani Dine. « Regularity in terms of Hyperideals ». Chinese Journal of Mathematics 2013 (30 décembre 2013) : 1–4. http://dx.doi.org/10.1155/2013/167037.

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This paper deals with the algebraic hypersystems. The notion of regularity of different type of algebraic systems has been introduced and characterized by different authors such as Iseki, Kovacs, and Lajos. We generalize this notion to algebraic hypersystems giving a unified generalization of the characterizations of Kovacs, Iseki, and Lajos. We generalize also the concept of ideal introducing the notion of j-hyperideal and hyperideal of an algebraic hypersystem. It turns out that the description of regularity in terms of hyperideals is intrinsic to associative hyperoperations in general. The main theorem generalizes to algebraic hypersystems some results on regular semigroups and regular rings and expresses a necessary and sufficient condition by means of principal hyperideals. Furthermore, two more theorems are obtained: one is concerned with a necessary and sufficient condition for an associative, commutative algebraic hypersystem to be regular and the other is concerned with nilpotent elements in the algebraic hypersystem.

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ERCAN, GÜLİN, et İSMAİL Ş. GÜLOĞLU. « A GENERALIZED FIXED POINT FREE AUTOMORPHISM OF PRIME POWER ORDER ». International Journal of Algebra and Computation 22, n^o 04 (juin 2012) : 1250029. http://dx.doi.org/10.1142/s0218196712500294.

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Let G be a finite group and α be an automorphism of G of order pn for an odd prime p. Suppose that α acts fixed point freely on every α-invariant p′-section of G, and acts trivially or exceptionally on every elementary abelian α-invariant p-section of G. It is proved that G is a solvable p-nilpotent group of nilpotent length at most n + 1, and this bound is best possible.

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Sattari, Mohammad Hossein, et Esmaeil Alizadeh. « Nilpotent Ideals in Generalized Amenable Banach Algebras ». Bulletin of the Iranian Mathematical Society 46, n^o 6 (8 février 2020) : 1745–51. http://dx.doi.org/10.1007/s41980-020-00355-z.

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Ballester-Bolinches, A., et Tatiana Pedraza. « On a Class of Generalized Nilpotent Groups ». Journal of Algebra 248, n^o 1 (février 2002) : 219–29. http://dx.doi.org/10.1006/jabr.2001.9035.

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Ribenboim, P. « Rings of generalized power series : Nilpotent elements ». Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 61, n^o 1 (décembre 1991) : 15–33. http://dx.doi.org/10.1007/bf02950748.

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Asiáin, M. J. « Classes of generalized nilpotent and soluble groups ». Siberian Mathematical Journal 37, n^o 3 (mai 1996) : 423–29. http://dx.doi.org/10.1007/bf02104843.

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AYADI, IMEN, HEDI BENAMOR et SAÏD BENAYADI. « LIE SUPERALGEBRAS WITH SOME HOMOGENEOUS STRUCTURES ». Journal of Algebra and Its Applications 11, n^o 05 (26 septembre 2012) : 1250095. http://dx.doi.org/10.1142/s0219498812500958.

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We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [A. Aubert, Structures affines et pseudo-métriques invariantes à gauche sur des groupes de Lie, Thèse, Université Montpellier II (1996)]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie superalgebras. Several examples are included to show the existence of homogeneous quadratic symplectic Lie superalgebras other than even-quadratic even-symplectic considered in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. We study the structures of even (respectively, odd)-quadratic odd (respectively, even)-symplectic Lie superalgebras and odd-quadratic odd-symplectic Lie superalgebras and we give its inductive descriptions in terms of quadratic generalized double extensions and odd quadratic generalized double extensions. This study complete the inductive descriptions of homogeneous quadratic symplectic Lie superalgebras started in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608]. Finally, we generalize to the case of homogeneous quadratic symplectic Lie superalgebras some relations between even-quadratic even-symplectic Lie superalgebras and Manin superalgebras established in [E. Barreiro and S. Benayadi, Quadratic symplectic Lie superalgebras and Lie bi-superalgebras, J. Algebra 321(2) (2009) 582–608].

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Lopes, Samuel A. « Non-Noetherian generalized Heisenberg algebras ». Journal of Algebra and Its Applications 16, n^o 04 (avril 2017) : 1750064. http://dx.doi.org/10.1142/s0219498817500645.

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In this note, we classify the non-Noetherian generalized Heisenberg algebras [Formula: see text] introduced in [R. Lü and K. Zhao, Finite-dimensional simple modules over generalized Heisenberg algebras, Linear Algebra Appl. 475 (2015) 276–291]. In case deg [Formula: see text] > 1, we determine all locally finite and also all locally nilpotent derivations of [Formula: see text] and describe the automorphism group of these algebras.

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Dokuchaev, Michael A., et Stanley O. Juriaans. « Finite Subgroups in Integral Group Rings ». Canadian Journal of Mathematics 48, n^o 6 (1 décembre 1996) : 1170–79. http://dx.doi.org/10.4153/cjm-1996-061-7.

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AbstractA p-subgroup version of the conjecture of Zassenhaus is proved for some finite solvable groups including solvable groups in which any Sylow p-subgroup is either abelian or generalized quaternion, solvable Frobenius groups, nilpotent-by-nilpotent groups and solvable groups whose orders are not divisible by the fourth power of any prime.

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Kong, Qingjun. « A Note on Hobby’s Theorem of Finite Groups ». Algebra 2013 (7 juillet 2013) : 1–3. http://dx.doi.org/10.1155/2013/135045.

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It is well known that the Frattini subgroups of any finite groups are nilpotent. If a finite group is not nilpotent, it is not the Frattini subgroup of a finite group. In this paper, we mainly discuss what kind of finite nilpotent groups cannot be the Frattini subgroup of some finite groups and give some results. Moreover, we generalize Hobby’s Theorem.

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Yu, Haoran. « Some sufficient and necessary conditions for p-supersolvablity and p-nilpotence of a finite group ». Journal of Algebra and Its Applications 16, n^o 03 (mars 2017) : 1750052. http://dx.doi.org/10.1142/s0219498817500529.

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BENTZ, WOLFRAM, et PETER MAYR. « SUPERNILPOTENCE PREVENTS DUALIZABILITY ». Journal of the Australian Mathematical Society 96, n^o 1 (30 septembre 2013) : 1–24. http://dx.doi.org/10.1017/s1446788713000517.

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AbstractWe address the question of the dualizability of nilpotent Mal’cev algebras, showing that nilpotent finite Mal’cev algebras with a nonabelian supernilpotent congruence are inherently nondualizable. In particular, finite nilpotent nonabelian Mal’cev algebras of finite type are nondualizable if they are direct products of algebras of prime power order. We show that these results cannot be generalized to nilpotent algebras by giving an example of a group expansion of infinite type that is nilpotent and nonabelian, but dualizable. To our knowledge this is the first construction of a nonabelian nilpotent dualizable algebra. It has the curious property that all its nonabelian finitary reducts with group operation are nondualizable. We were able to prove dualizability by utilizing a new clone theoretic approach developed by Davey, Pitkethly, and Willard. Our results suggest that supernilpotence plays an important role in characterizing dualizability among Mal’cev algebras.

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Srinivas, N., T. Bhanja et R. P. Malik. « (Anti)chiral Superfield Approach to Nilpotent Symmetries : Self-Dual Chiral Bosonic Theory ». Advances in High Energy Physics 2017 (2017) : 1–14. http://dx.doi.org/10.1155/2017/6138263.

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We exploit the beauty and strength of the symmetry invariant restrictions on the (anti)chiral superfields to derive the Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST, and (anti-)co-BRST symmetry transformations in the case of a two (1+1)-dimensional (2D) self-dual chiral bosonic field theory within the framework of augmented (anti)chiral superfield formalism. Our 2D ordinary theory is generalized onto a (2,2)-dimensional supermanifold which is parameterized by the superspace variable ZM=xμ,θ,θ¯, where xμ (with μ=0,1) are the ordinary 2D bosonic coordinates and (θ,θ¯) are a pair of Grassmannian variables with their standard relationships: θ2=θ¯2=0, θθ¯+θ¯θ=0. We impose the (anti-)BRST and (anti-)co-BRST invariant restrictions on the (anti)chiral superfields (defined on the (anti)chiral (2,1)-dimensional supersubmanifolds of the above general (2,2)-dimensional supermanifold) to derive the above nilpotent symmetries. We do not exploit the mathematical strength of the (dual-)horizontality conditions anywhere in our present investigation. We also discuss the properties of nilpotency, absolute anticommutativity, and (anti-)BRST and (anti-)co-BRST symmetry invariance of the Lagrangian density within the framework of our augmented (anti)chiral superfield formalism. Our observation of the absolute anticommutativity property is a completely novel result in view of the fact that we have considered only the (anti)chiral superfields in our present endeavor.

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