Results 21 to 30 of about 9,527,915 (298)
On the probability of zero divisor elements in group rings [PDF]
International Journal of Group Theory, 2022 Let $R$ be a non trivial finite commutative ring with identity and $G$ be a non trivial group. We denote by $P(RG)$ the probability that the product of two randomly chosen elements of a finite group ring $RG$ is zero. We show that $P(RG)
Haval Mohammed Salih
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On the ring of quotients of a group ring [PDF]
Proceedings of the American Mathematical Society, 1972 In this paper the following extension of a result of Martha Smith is proved. Theorem. Let K [ G ]
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On some commutative invariants of modules over minimax nilpotent groups
Доповiдi Нацiональної академiї наук України, 2022 In the paper we introduce a finite system of invariants for modules over minimax nilpotent groups which consists of classes of equivalent prime ideals of the group algebra of an Abelian minimax group. In particuly, introduced system of invariants allows
A.V. Tushev
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Smarandache Non-Associative (SNA-) rings [PDF]
, 2005 In this paper we introduce the concept of Smarandache non-associative rings, which we shortly denote as SNA-rings as derived from the general definition of a Smarandache Structure (i.e., a set A embedded with a week structure W such that a proper subset ...
Vasantha Kandasamy, W.B.
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On separable extensions of group rings and quaternion rings
International Journal of Mathematics and Mathematical Sciences, 1978 The purposes of the present paper are (1) to give a necessary and sufficient condition for the uniqueness of the separable idempotent for a separable group ring extension RG(R may be a non-commutative ring), and (2) to give a full description of the set ...
George Szeto
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LCD codes and LCP of codes from units of group rings
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 A linear code with complementary dual(LCD) is a linear code such that LCD codes are of greatimportance due to their wide range of applications in consumer electronics,storage systems and cryptography. Group rings have a rich source of units. Alsothe well-
Mehmet Emin Köroğlu
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On Reversible Group Rings [PDF]
Bulletin of the Australian Mathematical Society, 2006 Let G be an arbitrary finite group, R be a finite associative ring with identity and RG be the group ring. We show that ℤ2Q8 is the minimal reversible group ring which is not symmetric, and we also characterise the finite rings R for which RQ8 is reversible. The first result extends a result of Gutan and Kisielewicz which shows that ℤ2Q8 is the minimal
Li, Yuanlin +2 more
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Journal of Algebra, 2006 The authors' prime objective is to prove that the integral group ring \(\mathbb{Z} G\) of the non-Abelian finite group \(G\) of order prime to 6 contains two Bass cyclic units that generate a non-Abelian free group. A Bass cyclic unit of \(\mathbb{Z} G\) is an element of the form \[ (1+x+\cdots+x^{k-1})^m+d^{-1}(1-k^m)(1+x+\cdots+x^{d-1}), \] where \(x\
Gonçalves, J. Z., Passman, D. S.
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Group Rings Satisfying Generalized Engel Conditions
پژوهشهای ریاضی, 2020 Let R be a commutative ring with unity of characteristic r≥0 and G be a locally finite group. For each x and y in the group ring RG define [x,y]=xy-yx and inductively via [x ,_( n+1) y]=[[x ,_( n) y] , y].
Mojtaba Ramezan-Nassab
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Group rings for communications [PDF]
International Journal of Group Theory, 2015 This is a survey of some recent applications of abstract algebra, and in particular group rings, to the `communications' areas.
Ted Hurley
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