Articles de revues : « Noncommutative rings »

1

Buckley, S., et D. MacHale. « Noncommutative Anticommutative Rings ». Irish Mathematical Society Bulletin 0018 (1987) : 55–57. http://dx.doi.org/10.33232/bims.0018.55.57.

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2

Cohn, P. M. « NONCOMMUTATIVE NOETHERIAN RINGS ». Bulletin of the London Mathematical Society 20, n^o 6 (novembre 1988) : 627–29. http://dx.doi.org/10.1112/blms/20.6.627.

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3

KAUCIKAS, ALGIRDAS, et ROBERT WISBAUER. « NONCOMMUTATIVE HILBERT RINGS ». Journal of Algebra and Its Applications 03, n^o 04 (décembre 2004) : 437–43. http://dx.doi.org/10.1142/s0219498804000964.

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Commutative rings in which every prime ideal is the intersection of maximal ideals are called Hilbert (or Jacobson) rings. This notion was extended to noncommutative rings in two different ways by the requirement that prime ideals are the intersection of maximal or of maximal left ideals, respectively. Here we propose to define noncommutative Hilbert rings by the property that strongly prime ideals are the intersection of maximal ideals. Unlike for the other definitions, these rings can be characterized by a contraction property: R is a Hilbert ring if and only if for all n∈ℕ every maximal ideal [Formula: see text] contracts to a maximal ideal of R. This definition is also equivalent to [Formula: see text] being finitely generated as an [Formula: see text]-module, i.e., a liberal extension. This gives a natural form of a noncommutative Hilbert's Nullstellensatz. The class of Hilbert rings is closed under finite polynomial extensions and under integral extensions.

4

Alajbegovic̀, Jusuf H., et Nikolai I. Dubrovin. « Noncommutative prüfer rings ». Journal of Algebra 135, n^o 1 (novembre 1990) : 165–76. http://dx.doi.org/10.1016/0021-8693(90)90155-h.

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5

Dubrovin, N. I. « NONCOMMUTATIVE PRÜFER RINGS ». Mathematics of the USSR-Sbornik 74, n^o 1 (28 février 1993) : 1–8. http://dx.doi.org/10.1070/sm1993v074n01abeh003330.

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6

Wang, Jian, Yunxia Li et Jiangsheng Hu. « Noncommutative G-semihereditary rings ». Journal of Algebra and Its Applications 17, n^o 01 (janvier 2018) : 1850014. http://dx.doi.org/10.1142/s0219498818500147.

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In this paper, we introduce and study left (right) [Formula: see text]-semihereditary rings over any associative ring, and these rings are exactly [Formula: see text]-semihereditary rings defined by Mahdou and Tamekkante provided that [Formula: see text] is a commutative ring. Some new characterizations of left [Formula: see text]-semihereditary rings are given. Applications go in three directions. The first is to give a sufficient condition when a finitely presented right [Formula: see text]-module is Gorenstein flat if and only if it is Gorenstein projective provided that [Formula: see text] is left coherent. The second is to investigate the relationships between Gorenstein flat modules and direct limits of finitely presented Gorenstein projective modules. The third is to obtain some new characterizations of semihereditary rings, [Formula: see text]-[Formula: see text] rings and [Formula: see text] rings.

7

Ghorbani, A., et M. Naji Esfahani. « On noncommutative FGC rings ». Journal of Algebra and Its Applications 14, n^o 07 (24 avril 2015) : 1550109. http://dx.doi.org/10.1142/s0219498815501091.

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Many studies have been conducted to characterize commutative rings whose finitely generated modules are direct sums of cyclic modules (called FGC rings), however, the characterization of noncommutative FGC rings is still an open problem, even for duo rings. We study FGC rings in some special cases, it is shown that a local Noetherian ring R is FGC if and only if R is a principal ideal ring if and only if R is a uniserial ring, and if these assertions hold R is a duo ring. We characterize Noetherian duo FGC rings. In fact, it is shown that a duo ring R is a Noetherian left FGC ring if and only if R is a Noetherian right FGC ring, if and only if R is a principal ideal ring.

8

Zabavskii, B. V. « Noncommutative elementary divisor rings ». Ukrainian Mathematical Journal 39, n^o 4 (1988) : 349–53. http://dx.doi.org/10.1007/bf01060766.

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9

Gatalevich, A. I., et B. V. Zabavs'kii. « Noncommutative elementary divisor rings ». Journal of Mathematical Sciences 96, n^o 2 (août 1999) : 3013–16. http://dx.doi.org/10.1007/bf02169697.

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10

MacKenzie, Kenneth W. « Polycyclic group rings and unique factorisation rings ». Glasgow Mathematical Journal 36, n^o 2 (mai 1994) : 135–44. http://dx.doi.org/10.1017/s0017089500030676.

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The theory of unique factorisation in commutative rings has recently been extended to noncommutative Noetherian rings in several ways. Recall that an element x of a ring R is said to be normalif xR = Rx. We will say that an element p of a ring R is (completely) prime if p is a nonzero normal element of R and pR is a (completely) prime ideal. In [2], a Noetherian unique factorisation domain (or Noetherian UFD) is defined to be a Noetherian domain in which every nonzero prime ideal contains a completely prime element: this concept is generalised in [4], where a Noetherian unique factorisation ring(or Noetherian UFR) is defined as a prime Noetherian ring in which every nonzero prime ideal contains a nonzero prime element; note that it follows from the noncommutative version of the Principal Ideal Theorem that in a Noetherian UFR, if pis a prime element then the height of the prime ideal pR must be equal to 1. Surprisingly many classes of noncommutative Noetherian rings are known to be UFDs or UFRs: see [2] and [4] for details. This theory has recently been extended still further, to cover certain classes of non-Noetherian rings: see [3].

11

CHEN, WEIXING, et WENTING TONG. « ON NONCOMMUTATIVE VNL-RINGS AND GVNL-RINGS ». Glasgow Mathematical Journal 48, n^o 01 (24 mars 2006) : 11. http://dx.doi.org/10.1017/s0017089505002806.

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12

Reyes, Armando, et Héctor Suárez. « Skew Poincaré–Birkhoff–Witt extensions over weak compatible rings ». Journal of Algebra and Its Applications 19, n^o 12 (18 novembre 2019) : 2050225. http://dx.doi.org/10.1142/s0219498820502254.

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In this paper, we introduce weak [Formula: see text]-compatible rings and study skew Poincaré–Birkhoff–Witt extensions over these rings. We characterize the weak notion of compatibility for several noncommutative rings appearing in noncommutative algebraic geometry and some quantum algebras of theoretical physics. As a consequence of our treatment, we unify and extend results in the literature about Ore extensions and skew PBW extensions over compatible rings.

13

Bell, Howard E., et Abraham A. Klein. « Noncommutativity and noncentral zero divisors ». International Journal of Mathematics and Mathematical Sciences 22, n^o 1 (1999) : 67–74. http://dx.doi.org/10.1155/s0161171299220674.

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LetRbe a ring,Zits center, andDthe set of zero divisors. For finite noncommutative rings, it is known thatD\Z≠∅. We investigate the size of|D\Z|in this case and, also, in the case of infinite noncommutative rings withD\Z≠∅.

14

Li, Bingjun. « STRONGLY CLEAN MATRIX RINGS OVER NONCOMMUTATIVE LOCAL RINGS ». Bulletin of the Korean Mathematical Society 46, n^o 1 (31 janvier 2009) : 71–78. http://dx.doi.org/10.4134/bkms.2009.46.1.071.

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15

Sahai, Meena, et Sheere Farhat Ansari. « Lie centrally metabelian group rings over noncommutative rings ». Communications in Algebra 47, n^o 11 (11 avril 2019) : 4729–39. http://dx.doi.org/10.1080/00927872.2019.1593428.

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16

Formanek, Edward. « Book Review : Noncommutative Noetherian rings ». Bulletin of the American Mathematical Society 23, n^o 2 (1 octobre 1990) : 579–83. http://dx.doi.org/10.1090/s0273-0979-1990-15988-9.

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17

Çeken, S., M. Alkan et P. F. Smith. « Second Modules Over Noncommutative Rings ». Communications in Algebra 41, n^o 1 (31 janvier 2013) : 83–98. http://dx.doi.org/10.1080/00927872.2011.623026.

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18

Mialebama Bouesso, André Saint Eudes, et Djiby Sow. « Noncommutative Gröbner Bases over Rings ». Communications in Algebra 43, n^o 2 (25 août 2014) : 541–57. http://dx.doi.org/10.1080/00927872.2012.738340.

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19

Bailey, Abigail C., et John A. Beachy. « On noncommutative piecewise Noetherian rings ». Communications in Algebra 45, n^o 6 (7 octobre 2016) : 2662–72. http://dx.doi.org/10.1080/00927872.2016.1233232.

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20

Yekutieli, Amnon, et James J. Zhang. « Residue complexes over noncommutative rings ». Journal of Algebra 259, n^o 2 (janvier 2003) : 451–93. http://dx.doi.org/10.1016/s0021-8693(02)00579-3.

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21

Tuganbaev, A. A. « Comultiplication Modules over Noncommutative Rings ». Journal of Mathematical Sciences 191, n^o 5 (17 mai 2013) : 743–47. http://dx.doi.org/10.1007/s10958-013-1357-y.

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22

Lunts, V. A., et A. L. Rosenberg. « Differential operators on noncommutative rings ». Selecta Mathematica 3, n^o 3 (septembre 1997) : 335–59. http://dx.doi.org/10.1007/s000290050014.

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23

Gr�ter, Joachim. « On noncommutative Pr�fer rings ». Archiv der Mathematik 46, n^o 5 (mai 1986) : 402–7. http://dx.doi.org/10.1007/bf01210779.

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24

Johnson, Keith. « $P$-orderings of noncommutative rings ». Proceedings of the American Mathematical Society 143, n^o 8 (1 avril 2015) : 3265–79. http://dx.doi.org/10.1090/s0002-9939-2015-12377-5.

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25

Bell, Howard E., et Abraham A. Klein. « Extremely noncommutative elements in rings ». Monatshefte für Mathematik 153, n^o 1 (12 octobre 2007) : 19–24. http://dx.doi.org/10.1007/s00605-007-0505-1.

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26

Annin, Scott. « Attached primes over noncommutative rings ». Journal of Pure and Applied Algebra 212, n^o 3 (mars 2008) : 510–21. http://dx.doi.org/10.1016/j.jpaa.2007.05.024.

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27

Wauters, P., et E. Jespers. « Examples Of noncommutative krull rings ». Communications in Algebra 14, n^o 5 (janvier 1986) : 819–32. http://dx.doi.org/10.1080/00927878608823338.

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28

Jørgensen, Peter. « Gorenstein homomorphisms of noncommutative rings ». Journal of Algebra 211, n^o 1 (janvier 1999) : 240–67. http://dx.doi.org/10.1006/jabr.1998.7608.

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29

Wu, Q. S., et J. J. Zhang. « Homological Identities for Noncommutative Rings ». Journal of Algebra 242, n^o 2 (août 2001) : 516–35. http://dx.doi.org/10.1006/jabr.2001.8817.

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30

Quinn, Declan. « Integral extensions of noncommutative rings ». Israel Journal of Mathematics 73, n^o 1 (février 1991) : 113–21. http://dx.doi.org/10.1007/bf02773430.

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31

Dobbs, David E., et Noômen Jarboui. « Normal pairs of noncommutative rings ». Ricerche di Matematica 69, n^o 1 (11 juin 2019) : 95–109. http://dx.doi.org/10.1007/s11587-019-00450-2.

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32

Derr, J. B., G. F. Orr et Paul S. Peck. « Noncommutative rings of order p4 ». Journal of Pure and Applied Algebra 97, n^o 2 (novembre 1994) : 109–16. http://dx.doi.org/10.1016/0022-4049(94)00015-8.

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33

Nath, Rajat Kanti, Monalisha Sharma, Parama Dutta et Yilun Shang. « On r-Noncommuting Graph of Finite Rings ». Axioms 10, n^o 3 (19 septembre 2021) : 233. http://dx.doi.org/10.3390/axioms10030233.

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Let R be a finite ring and r∈R. The r-noncommuting graph of R, denoted by ΓRr, is a simple undirected graph whose vertex set is R and two vertices x and y are adjacent if and only if [x,y]≠r and [x,y]≠−r. In this paper, we obtain expressions for vertex degrees and show that ΓRr is neither a regular graph nor a lollipop graph if R is noncommutative. We characterize finite noncommutative rings such that ΓRr is a tree, in particular a star graph. It is also shown that ΓR1r and ΓR2ψ(r) are isomorphic if R1 and R2 are two isoclinic rings with isoclinism (ϕ,ψ). Further, we consider the induced subgraph ΔRr of ΓRr (induced by the non-central elements of R) and obtain results on clique number and diameter of ΔRr along with certain characterizations of finite noncommutative rings such that ΔRr is n-regular for some positive integer n. As applications of our results, we characterize certain finite noncommutative rings such that their noncommuting graphs are n-regular for n≤6.

34

Markov, Viktor T., et Askar A. Tuganbaev. « Centrally essential rings ». Discrete Mathematics and Applications 29, n^o 3 (26 juin 2019) : 189–94. http://dx.doi.org/10.1515/dma-2019-0017.

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Abstract A centrally essential ring is a ring which is an essential extension of its center (we consider the ring as a module over its center). We give several examples of noncommutative centrally essential rings and describe some properties of centrally essential rings.

35

Coutinho, S. C., et J. C. McConnell. « The Quest for Quotient Rings (Of Noncommutative Noetherian Rings) ». American Mathematical Monthly 110, n^o 4 (avril 2003) : 298. http://dx.doi.org/10.2307/3647879.

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36

Coutinho, S. C., et J. C. McConnell. « The Quest for Quotient Rings (of Noncommutative Noetherian Rings) ». American Mathematical Monthly 110, n^o 4 (avril 2003) : 298–313. http://dx.doi.org/10.1080/00029890.2003.11919966.

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37

Sánchez, Javier. « Obtaining free group algebras in division rings generated by group graded rings ». Journal of Algebra and Its Applications 17, n^o 10 (octobre 2018) : 1850194. http://dx.doi.org/10.1142/s0219498818501943.

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We give sufficient conditions for the existence of noncommutative free group algebras in division rings generated by group graded rings. We also relate our conclusions to already existing results on the subject improving some of them.

38

Small, Lance, et T. Y. Lam. « A First Course in Noncommutative Rings. » American Mathematical Monthly 100, n^o 7 (août 1993) : 698. http://dx.doi.org/10.2307/2323906.

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39

Denton, Brian, et T. Y. Lam. « A First Course in Noncommutative Rings ». Mathematical Gazette 86, n^o 505 (mars 2002) : 177. http://dx.doi.org/10.2307/3621626.

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40

Huh, Chan, Nam-Kyun Kim et Yang Lee. « AN ANDERSON'S THEOREM ON NONCOMMUTATIVE RINGS ». Bulletin of the Korean Mathematical Society 45, n^o 4 (30 novembre 2008) : 797–800. http://dx.doi.org/10.4134/bkms.2008.45.4.797.

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41

Kim, Byung-Ok, et Yang Lee. « MINIMAL NONCOMMUTATIVE REVERSIBLE AND REFLEXIVE RINGS ». Bulletin of the Korean Mathematical Society 48, n^o 3 (31 mai 2011) : 611–16. http://dx.doi.org/10.4134/bkms.2011.48.3.611.

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42

Hajarnavis, C. R. « AN INTRODUCTION TO NONCOMMUTATIVE NOETHERIAN RINGS ». Bulletin of the London Mathematical Society 23, n^o 1 (janvier 1991) : 91–93. http://dx.doi.org/10.1112/blms/23.1.91.

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43

Cimprič, Jaka. « HIGHER PRODUCT LEVELS OF NONCOMMUTATIVE RINGS ». Communications in Algebra 29, n^o 1 (21 mars 2001) : 193–200. http://dx.doi.org/10.1081/agb-100000794.

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44

Komatsu, Hiroaki. « QUASI-SEPARABLE EXTENSIONS OF NONCOMMUTATIVE RINGS ». Communications in Algebra 29, n^o 3 (28 février 2001) : 1011–19. http://dx.doi.org/10.1081/agb-100001663.

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45

CHERCHEM, AHMED, TAREK GARICI et ABDELKADER NECER. « LINEAR RECURRING SEQUENCES OVER NONCOMMUTATIVE RINGS ». Journal of Algebra and Its Applications 11, n^o 02 (avril 2012) : 1250040. http://dx.doi.org/10.1142/s0219498811005646.

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Contrary to the commutative case, the set of linear recurring sequences with values in a module over a noncommutative ring is no more a module for the usual operations. We show the stability of these operations when the ring is a matrix ring or a division ring. In the case of a finite dimensional division ring over its center, we give an algorithm for the determination of a recurrence relation for the sum of two linear recurring sequences.

46

Dosi, Anar. « Noncommutative Localizations of Lie-Complete Rings ». Communications in Algebra 44, n^o 11 (16 juin 2016) : 4892–944. http://dx.doi.org/10.1080/00927872.2015.1130135.

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47

Golod, E. S. « On noncommutative Gröbner bases over rings ». Journal of Mathematical Sciences 140, n^o 2 (janvier 2007) : 239–42. http://dx.doi.org/10.1007/s10958-007-0420-y.

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48

Ferens-Sorotskiy, E. V. « Weierstrass preparation theorem for noncommutative rings ». Journal of Mathematical Sciences 161, n^o 4 (19 août 2009) : 597–601. http://dx.doi.org/10.1007/s10958-009-9587-8.

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49

Navarro, Gabriel, Oscar Cortadellas et F. J. Lobillo. « Prime fuzzy ideals over noncommutative rings ». Fuzzy Sets and Systems 199 (juillet 2012) : 108–20. http://dx.doi.org/10.1016/j.fss.2011.11.002.

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50

Öneş, O., et M. Alkan. « The Radical Formula for Noncommutative Rings ». Ukrainian Mathematical Journal 71, n^o 9 (février 2020) : 1419–28. http://dx.doi.org/10.1007/s11253-020-01723-y.

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Articles de revues sur le sujet « Noncommutative rings »

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