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Journal articles on the topic 'Engel conditions'

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Published: 10 March 2023

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1

RAMEZAN-NASSAB, M., and D. KIANI. "RINGS SATISFYING GENERALIZED ENGEL CONDITIONS." Journal of Algebra and Its Applications 11, no. 06 (November 14, 2012): 1250121. http://dx.doi.org/10.1142/s0219498812501216.

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Let R be an associative ring and let x, y ∈ R. Define the generalized commutators as follows: [x, 0y] = x and [x, ky] = [x, k-1y]y - y[x, k-1y](k = 1, 2, …). In this paper we study some generalized Engel rings, i.e. [Formula: see text]-rings (satisfying [xm(x, y), k(x, y)y] = 0), [Formula: see text]-rings (satisfying [xm(x, y), k(x, y)yn(x, y)] = 0) and [Formula: see text]-rings (satisfying [xm(x, y), k(x, y)yn(x, y)]r(x, y) = 0). Among other results, it is proved that every Artinian [Formula: see text]-ring is strictly Lie-nilpotent. Also, we show that in each of the following cases R has nil commutator ideal: (1) if R is a [Formula: see text]-ring with unity and k, n independent of y; (2) if R is a locally bounded [Formula: see text]-ring (defined below); (3) if R is an algebraic algebra over a field in which R* is a bounded Engel group or a soluble group.

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2

Lanski, Charles. "Skew Derivations and Engel Conditions." Communications in Algebra 42, no. 1 (October 18, 2013): 139–52. http://dx.doi.org/10.1080/00927872.2012.707719.

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3

Mattarei, Sandro. "Engel conditions and symmetric tensors." Linear and Multilinear Algebra 59, no. 4 (April 2011): 441–49. http://dx.doi.org/10.1080/03081081003621295.

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4

Amberg, Bernhard, and Yaroslav P. Sysak. "Radical Rings with Engel Conditions." Journal of Algebra 231, no. 1 (September 2000): 364–73. http://dx.doi.org/10.1006/jabr.2000.8370.

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5

Picelli, Enrico. "Semilocal rings with Engel conditions." Archiv der Mathematik 87, no. 4 (October 2006): 289–94. http://dx.doi.org/10.1007/s00013-006-1731-9.

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6

Fan, Yun, and Jinke Hai. "A Note on ?-Engel Conditions." Southeast Asian Bulletin of Mathematics 25, no. 2 (October 2001): 223–28. http://dx.doi.org/10.1007/s10012-001-0223-x.

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7

Shumyatsky, Pavel. "Orderable groups with Engel-like conditions." Journal of Algebra 499 (April 2018): 311–20. http://dx.doi.org/10.1016/j.jalgebra.2017.12.018.

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8

Koşan, M. Tamer, Tsiu-Kwen Lee, and Yiqiang Zhou. "Identities with Engel conditions on derivations." Monatshefte für Mathematik 165, no. 3-4 (October 21, 2010): 543–56. http://dx.doi.org/10.1007/s00605-010-0252-6.

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9

Calin, Ovidiu, Der-Chen Chang, and Jishan Hu. "Integrability conditions on Engel-type manifolds." Analysis and Mathematical Physics 5, no. 3 (June 23, 2015): 217–31. http://dx.doi.org/10.1007/s13324-015-0107-3.

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10

Ramezan-Nassab, Mojtaba. "Group Rings Satisfying Generalized Engel Conditions." Mathematical Researches 6, no. 1 (May 1, 2020): 57–64. http://dx.doi.org/10.52547/mmr.6.1.57.

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11

Chuang, Chen-Lian, Ming-Chu Chou, and Cheng-Kai Liu. "Skew derivations with annihilating Engel conditions." Publicationes Mathematicae Debrecen 68, no. 1-2 (January 1, 2006): 161–70. http://dx.doi.org/10.5486/pmd.2006.3255.

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12

QUEK, S. G., K. B. WONG, and P. C. WONG. "ON n-ENGEL PAIR SATISFYING CERTAIN CONDITIONS." Journal of Algebra and Its Applications 13, no. 04 (January 9, 2014): 1350135. http://dx.doi.org/10.1142/s0219498813501351.

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Let G be a group and h, g ∈ G. The 2-tuple (h, g) is said to be an n-Engel pair, n ≥ 2, if h = [h,n g], g = [g,n h] and h ≠ 1. In this paper, we prove that if (h, g) is an n-Engel pair, hgh-2gh = ghg and ghg-2hg = hgh, then n = 2k where k = 4 or k ≥ 6. Furthermore, the subgroup generated by {h, g} is determined for k = 4, 6, 7 and 8.

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13

Chang, Jui-Chi. "GENERALIZED SKEW DERIVATIONS WITH ANNIHILATING ENGEL CONDITIONS." Taiwanese Journal of Mathematics 12, no. 7 (October 2008): 1641–50. http://dx.doi.org/10.11650/twjm/1500405076.

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14

Lee, Pjek-Hwee, and Tsiu-Kwen Lee. "Derivations with Engel conditions on multilinear polynomials." Proceedings of the American Mathematical Society 124, no. 9 (1996): 2625–29. http://dx.doi.org/10.1090/s0002-9939-96-03351-5.

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15

Riley, David M. "Generalised nilpotence conditions inn-engel lie algebras." Communications in Algebra 28, no. 10 (January 2000): 4619–34. http://dx.doi.org/10.1080/00927870008827108.

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16

Chen, Hung-Yuan. "Generalized Derivations with Engel Conditions on Polynomials." Communications in Algebra 39, no. 10 (October 2011): 3709–21. http://dx.doi.org/10.1080/00927872.2010.510817.

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17

Bastos, Raimundo, and Pavel Shumyatsky. "On profinite groups with Engel-like conditions." Journal of Algebra 427 (April 2015): 215–25. http://dx.doi.org/10.1016/j.jalgebra.2015.01.002.

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18

Kappe, Luise-Charlotte, and Gunnar Traustason. "Subnormality conditions in non-torsion groups." Bulletin of the Australian Mathematical Society 59, no. 3 (June 1999): 459–65. http://dx.doi.org/10.1017/s0004972700033141.

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According to results of Heineken and Stadelmann, a non-torsion group is a 2-Baer group if and only if it is 2-Engel, and it has all subgroups 2-subnormal if and only if it is nilpotent of class 2. We extend some of these results to values of n greater than 2. Any non-torsion group which is an n-Baer group is an n-Engel group. The converse holds for n = 3, and for all n in the case of metabelian groups. A non-torsion group without involutions having all subgroups 3-subnormal has nilpotency class 4, and this bound is sharp.

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19

HAVAS, GEORGE, and M. R. VAUGHAN-LEE. "4-ENGEL GROUPS ARE LOCALLY NILPOTENT." International Journal of Algebra and Computation 15, no. 04 (August 2005): 649–82. http://dx.doi.org/10.1142/s0218196705002475.

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Questions about nilpotency of groups satisfying Engel conditions have been considered since 1936, when Zorn proved that finite Engel groups are nilpotent. We prove that 4-Engel groups are locally nilpotent. Our proof makes substantial use of both hand and machine calculations.

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20

Liu, Cheng-Kai, and Wen-Kwei Shiue. "On the Centralizers of Derivations with Engel Conditions." Communications in Algebra 41, no. 5 (May 20, 2013): 1636–46. http://dx.doi.org/10.1080/00927872.2011.649223.

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21

Meriano, Maurizio, and Chiara Nicotera. "On Certain Weak Engel-Type Conditions in Groups." Communications in Algebra 42, no. 10 (May 14, 2014): 4241–47. http://dx.doi.org/10.1080/00927872.2013.806522.

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22

Bastos, Raimundo. "On Residually Finite Groups with Engel-like Conditions." Communications in Algebra 44, no. 10 (June 3, 2016): 4177–84. http://dx.doi.org/10.1080/00927872.2015.1087014.

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23

MORAVEC, PRIMOŽ. "ON NONABELIAN TENSOR ANALOGUES OF 2-ENGEL CONDITIONS." Glasgow Mathematical Journal 47, no. 1 (February 2005): 77–86. http://dx.doi.org/10.1017/s0017089504002083.

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24

Liu, Cheng-Kai. "DERIVATIONS WITH ENGEL AND ANNIHILATOR CONDITIONS ON MULTILINEAR POLYNOMIALS." Communications in Algebra 33, no. 3 (March 9, 2005): 719–25. http://dx.doi.org/10.1081/agb-200049880.

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25

Abdollahi, Alireza. "Some Engel conditions on infinite subsets of certain groups." Bulletin of the Australian Mathematical Society 62, no. 1 (August 2000): 141–48. http://dx.doi.org/10.1017/s0004972700018554.

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Let k be a positive integer. We denote by ɛk(∞) the class of all groups in which every infinite subset contains two distinct elements x, y such that [x,k y] = 1. We say that a group G is an -group provided that whenever X, Y are infinite subsets of G, there exists x ∈ X, y ∈ Y such that [x,k y] = 1. Here we prove that:(1) If G is a finitely generated soluble group, then G ∈ ɛ3(∞) if and only if G is finite by a nilpotent group in which every two generator subgroup is nilpotent of class at most 3.(2) If G is a finitely generated metabelian group, then G ∈ ɛk(∞) if and only if G/Zk (G) is finite, where Zk (G) is the (k + 1)-th term of the upper central series of G.(3) If G is a finitely generated soluble ɛk(∞)-group, then there exists a positive integer t depending only on k such that G/Zt (G) is finite.(4) If G is an infinite -group in which every non-trivial finitely generated subgroup has a non-trivial finite quotient, then G is k-Engel. In particular, G is locally nilpotent.

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26

Shiue, Wen-Kwei. "Annihilators of derivations with Engel conditions on lie ideals." Rendiconti del Circolo Matematico di Palermo 52, no. 3 (October 2003): 505–9. http://dx.doi.org/10.1007/bf02872768.

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27

Albaş, Emine, Nurcan Argaç, and Vincenzo De Filippis. "Generalized Derivations with Engel Conditions on One-Sided Ideals." Communications in Algebra 36, no. 6 (May 27, 2008): 2063–71. http://dx.doi.org/10.1080/00927870801949328.

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28

Wang, Yu. "A Generalization of Engel Conditions with Derivations in Rings." Communications in Algebra 39, no. 8 (August 2011): 2690–96. http://dx.doi.org/10.1080/00927872.2010.489536.

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29

Huang, Shuliang. "Derivations with engel conditions in prime and semiprime rings." Czechoslovak Mathematical Journal 61, no. 4 (December 2011): 1135–40. http://dx.doi.org/10.1007/s10587-011-0053-7.

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30

Chacron, M., and T. K. Lee. "Open questions concerning antiautomorphisms of division rings with quasi-generalized Engel conditions." Journal of Algebra and Its Applications 18, no. 09 (July 17, 2019): 1950167. http://dx.doi.org/10.1142/s0219498819501676.

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Let [Formula: see text] be a noncommutative division ring with center [Formula: see text], which is algebraic, that is, [Formula: see text] is an algebraic algebra over the field [Formula: see text]. Let [Formula: see text] be an antiautomorphism of [Formula: see text] such that (i) [Formula: see text], all [Formula: see text], where [Formula: see text] and [Formula: see text] are positive integers depending on [Formula: see text]. If, further, [Formula: see text] has finite order, it was shown in [M. Chacron, Antiautomorphisms with quasi-generalised Engel condition, J. Algebra Appl. 17(8) (2018) 1850145 (19 pages)] that [Formula: see text] is commuting, that is, [Formula: see text], all [Formula: see text]. Posed in [M. Chacron, Antiautomorphisms with quasi-generalised Engel condition, J. Algebra Appl. 17(8) (2018) 1850145 (19 pages)] is the question which asks as to whether the finite order requirement on [Formula: see text] can be dropped. We provide here an affirmative answer to the question. The second major result of this paper is concerned with a nonnecessarily algebraic division ring [Formula: see text] with an antiautomorphism [Formula: see text] satisfying the stronger condition (ii) [Formula: see text], all [Formula: see text], where [Formula: see text] and [Formula: see text] are fixed positive integers. It was shown in [T.-K. Lee, Anti-automorphisms satisfying an Engel condition, Comm. Algebra 45(9) (2017) 4030–4036] that if, further, [Formula: see text] has finite order then [Formula: see text] is commuting. We show here, that again the finite order assumption on [Formula: see text] can be lifted answering thus in the affirmative the open question (see Question 2.11 in [T.-K. Lee, Anti-automorphisms satisfying an Engel condition, Comm. Algebra 45(9) (2017) 4030–4036]).

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31

QUEK, S. G., K. B. WONG, and P. C. WONG. "ON CERTAIN PAIRS OF NON-ENGEL ELEMENTS IN FINITE GROUPS." Journal of Algebra and Its Applications 12, no. 05 (May 7, 2013): 1250213. http://dx.doi.org/10.1142/s0219498812502131.

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Let G be a group and h, g ∈ G. The 2-tuple (h, g) is said to be an n-Engel pair if h = [h,n g] and g = [g,n h]. In this paper, we will study the subgroup generated by the n-Engel pair under certain conditions.

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32

Chiappori, Pierre-Andre, and Jesse Naidoo. "The Engel Curves of Non-Cooperative Households." Economic Journal 130, no. 627 (January 8, 2020): 653–74. http://dx.doi.org/10.1093/ej/uez069.

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Abstract We provide a set of necessary and sufficient conditions for a system of Engel curves to have been generated by a non-cooperative model of family behaviour. These conditions fully characterise the local behaviour of household-level consumption in the cross-section, i.e., as a function of total income and distribution factors. In this setting, any demand system compatible with a non-cooperative model is also compatible with a collective model, but the converse is not true. We describe how these nested conditions may be tested using standard instrumental-variables strategies.

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33

Mohammadzadeh, Elahe, and Rajab Ali Borzooei. "Engel, Nilpotent and Solvable BCI-algebras." Analele Universitatii "Ovidius" Constanta - Seria Matematica 27, no. 1 (March 1, 2019): 169–92. http://dx.doi.org/10.2478/auom-2019-0009.

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Abstract In this paper, we define the concepts of Engel, nilpotent and solvable BCI-algebras and investigate some of their properties. Specially, we prove that any BCK-algebra is a 2-Engel. Then we define the center of a BCI-algebra and prove that in a nilpotent BCI-algebra X, each minimal closed ideal of X is contained in the center of X. In addition, with some conditions, we show that every finite BCI-algebra is solvable. Finally, we investigate the relations among Engel, nilpotent and solvable BCI(BCK)-algebras.

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34

Pehlivan, Taylan, and Emine Albas. "Annihilators of skew derivations with Engel conditions on prime rings." Czechoslovak Mathematical Journal 70, no. 2 (December 16, 2019): 587–603. http://dx.doi.org/10.21136/cmj.2019.0412-18.

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35

Chou, Ming-Chu, and Cheng-Kai Liu. "Annihilators of Skew Derivations with Engel Conditions on Lie Ideals." Communications in Algebra 44, no. 2 (December 15, 2015): 898–911. http://dx.doi.org/10.1080/00927872.2014.990028.

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36

Chacron, M. "More on involutions with local Engel or power commuting conditions." Communications in Algebra 45, no. 8 (October 28, 2016): 3503–14. http://dx.doi.org/10.1080/00927872.2016.1237641.

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37

De Filippis, Vincenzo, and Giovanni Scudo. "Annihilating and Engel conditions on right ideals with generalized derivations." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 57, no. 1 (January 29, 2015): 155–72. http://dx.doi.org/10.1007/s13366-015-0236-8.

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38

Shiue, Wen-Kwei. "Annihilators of derivations with Engel conditions on one-sided ideals." Publicationes Mathematicae Debrecen 62, no. 1-2 (January 1, 2003): 237–43. http://dx.doi.org/10.5486/pmd.2003.2751.

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39

De Filippis, Vincenzo. "Engel-Type Conditions Involving Two Generalized Skew Derivations in Prime Rings." Communications in Algebra 44, no. 7 (February 18, 2016): 3139–52. http://dx.doi.org/10.1080/00927872.2015.1065849.

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40

Scudo, Giovanni. "Generalized derivations with annihilating and centralizing Engel conditions on Lie ideals." Rendiconti del Circolo Matematico di Palermo 61, no. 3 (June 13, 2012): 343–53. http://dx.doi.org/10.1007/s12215-012-0094-2.

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41

Acciarri, Cristina, and Danilo Silveira. "Engel-like conditions in fixed points of automorphisms of profinite groups." Annali di Matematica Pura ed Applicata (1923 -) 199, no. 1 (June 10, 2019): 187–97. http://dx.doi.org/10.1007/s10231-019-00872-7.

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42

Demir, Cagri, and Nurcan Argac. "A RESULT ON GENERALIZED DERIVATIONS WITH ENGEL CONDITIONS ON ONE-SIDED IDEALS." Journal of the Korean Mathematical Society 47, no. 3 (May 1, 2010): 483–94. http://dx.doi.org/10.4134/jkms.2010.47.3.483.

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43

Rania, Francesco. "A note on sandwich Engel conditions on Lie ideals in semiprime rings." International Mathematical Forum 8 (2013): 1503–8. http://dx.doi.org/10.12988/imf.2013.37149.

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44

MAL'CEV, YURI N. "JUST NON COMMUTATIVE VARIETIES OF OPERATOR ALGEBRAS AND RINGS WITH SOME CONDITIONS ON NILPOTENT ELEMENTS." Tamkang Journal of Mathematics 27, no. 1 (March 1, 1996): 59–65. http://dx.doi.org/10.5556/j.tkjm.27.1996.4362.

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In §1 it is given a classification of Just noncommutative varieties of associative over algebras over commutative Jacobson ring with unity. In [1], [4] are given different proofs of the commutativity of a finite ring with central nilpotent elements. In §2 we give generalizations of these results for infinite rings and for the case of Engel identity.

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45

Liau, Pao-Kuei, and Cheng-Kai Liu. "An Engel condition with b-generalized derivations for Lie ideals." Journal of Algebra and Its Applications 17, no. 03 (February 5, 2018): 1850046. http://dx.doi.org/10.1142/s0219498818500469.

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Let [Formula: see text] be a prime ring with the extended centroid [Formula: see text], [Formula: see text] a noncommutative Lie ideal of [Formula: see text] and [Formula: see text] a nonzero [Formula: see text]-generalized derivation of [Formula: see text]. For [Formula: see text], let [Formula: see text]. We prove that if [Formula: see text] for all [Formula: see text], where [Formula: see text] are fixed positive integers, then there exists [Formula: see text] such that [Formula: see text] for all [Formula: see text] except when [Formula: see text], the [Formula: see text] matrix ring over a field [Formula: see text]. The analogous result for generalized skew derivations is also described. Our theorems naturally generalize the cases of derivations and skew derivations obtained by Lanski in [C. Lanski, An Engel condition with derivation, Proc. Amer. Math. Soc. 118 (1993), 75–80, Skew derivations and Engel conditions, Comm. Algebra 42 (2014), 139–152.]

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46

Dhara, Basudeb, and Vincenzo De Filippis. "Engel conditions of generalized derivations on left ideals and Lie ideals in prime rings." Communications in Algebra 48, no. 1 (July 5, 2019): 154–67. http://dx.doi.org/10.1080/00927872.2019.1635608.

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47

Mohammadzadeh, E., G. Muhiuddin, J. Zhan, and R. A. Borzooei. "Nilpotent fuzzy lie ideals." Journal of Intelligent & Fuzzy Systems 39, no. 3 (October 7, 2020): 4071–79. http://dx.doi.org/10.3233/jifs-200211.

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In this paper, we introduce a new definition for nilpotent fuzzy Lie ideal, which is a well-defined extension of nilpotent Lie ideal in Lie algebras, and we name it a good nilpotent fuzzy Lie ideal. Then we prove that a Lie algebra is nilpotent if and only if any fuzzy Lie ideal of it, is a good nilpotent fuzzy Lie ideal. In particular, we construct a nilpotent Lie algebra via a good nilpotent fuzzy Lie ideal. Also, we prove that with some conditions, every good nilpotent fuzzy Lie ideal is finite. Finally, we define an Engel fuzzy Lie ideal, and we show that every Engel fuzzy Lie ideal of a finite Lie algebra is a good nilpotent fuzzy Lie ideal. We think that these notions could be useful to solve some problems of Lie algebras with nilpotent fuzzy Lie ideals.

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48

Dhara, Basudeb, Krishna Gopal Pradhan, and Shailesh Kumar Tiwari. "Engel type identities with generalized derivations in prime rings." Asian-European Journal of Mathematics 11, no. 04 (August 2018): 1850055. http://dx.doi.org/10.1142/s1793557118500559.

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Let [Formula: see text] be a noncommutative prime ring with its Utumi ring of quotients [Formula: see text], [Formula: see text] the extended centroid of [Formula: see text], [Formula: see text] a generalized derivation of [Formula: see text] and [Formula: see text] a nonzero ideal of [Formula: see text]. If [Formula: see text] satisfies any one of the following conditions: (i) [Formula: see text], [Formula: see text], [Formula: see text], (ii) [Formula: see text], where [Formula: see text] is a fixed integer, then one of the following holds: (1) there exists [Formula: see text] such that [Formula: see text] for all [Formula: see text]; (2) [Formula: see text] satisfies [Formula: see text] and there exist [Formula: see text] and [Formula: see text] such that [Formula: see text] for all [Formula: see text]; (3) char [Formula: see text], [Formula: see text] satisfies [Formula: see text] and there exist [Formula: see text] and an outer derivation [Formula: see text] of [Formula: see text] such that [Formula: see text] for all [Formula: see text].

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49

Engel, Richard, Clain Jones, and Rosie Wallander. "Ammonia volatilization losses were small after mowing field peas in dry conditions." Canadian Journal of Soil Science 93, no. 2 (May 2013): 239–42. http://dx.doi.org/10.4141/cjss2012-091.

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Engel, R., Jones, C. and Wallander, R. 2013. Ammonia volatilization losses were small after mowing field peas in dry conditions. Can. J. Soil Sci. 93: 239–242. Ammonia losses following termination of peas (Pisum sativum L.) by mowing were measured using a micrometeorological mass-balance approach. Field trials were conducted during two seasons in a semiarid climate. Plant N in the above ground biomass was 105 and 79 kg N ha−1 in 2011 and 2012, respectively. Vertical NH3 flux estimates were nominal (0.3 to 1.7 g N ha−1 h−1) in the 2 wk following mowing. Cumulative NH3 loss represented 0.3 to 0.5% of the N in plant biomass, indicating that N fertility was not diminished by NH3 volatilization in this dry climate.

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50

Rasyid, Mohtar, Anita Kristina, Sutikno ., Sunaryati ., and Tutik Yuliani. "Poverty Conditions and Patterns of Consumption: An Engel Function Analysis in East Java and Bali, Indonesia." Asian Economic and Financial Review 10, no. 10 (2020): 1062–76. http://dx.doi.org/10.18488/journal.aefr.2020.1010.1062.1076.

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