Results 21 to 30 of about 225,341 (216)
On the primitive irreducible representations of finitely generated nilpotent groups
Доповiдi Нацiональної академiї наук України, 2021 We develop some tecniques whish allow us to apply the methods of commutative algebra for studing the representations of nilpotent groups. Using these methods, in particular, we show that any irreducible representation of a finitely generated nilpotent ...
A.V. Tushev
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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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Public Key Protocols over Skew Dihedral Group Rings
Mathematics, 2022 This paper introduces skew dihedral group rings and their applications for public-key cryptography. We present a specific skew group ring that is the underlying algebraic platform for our cryptographic constructions.
Javier de la Cruz +2 more
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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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Journal of Pure and Applied Algebra, 2006 An associative ring \(R\) with identity is called left morphic if for every element \(a\in R\) there exists \(b\in R\) such that \(l_R(a)=Rb\) and \(l_R(b)=Ra\), where \(l_R(a)\) denotes the left annihilator of \(a\) in \(R\). The ring \(R\) is said to be strongly left morphic if every matrix ring \(M_n(R)\) is left morphic [\textit{W. K.
Chen, Jianlong +2 more
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On Idempotent Units in Commutative Group Rings
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2020 Special elements as units, which are defined utilizing idempotent elements, have a very crucial place in a commutative group ring. As a remark, we note that an element is said to be idempotent if r^2=r in a ring. For a group ring RG, idempotent units are
Ömer Küsmüş
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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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On Galois projective group rings
International Journal of Mathematics and Mathematical Sciences, 1991 Let A be a ring with 1, C the center of A and G′ an inner automorphism group of A induced by {Uα in A/α in a finite group G whose order is invertible}.
George Szeto, Linjun Ma
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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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Generalizations of Morphic Group Rings
International Journal of Mathematics and Mathematical Sciences, 2007 An element a in a ring R is called left morphic if there exists b∈R such that 1R(a)=Rb and 1R(b)=Ra. R is called left morphic if every element of R is left morphic.
Libo Zan, Jianlong Chen, Qinghe Huang
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