Results 31 to 40 of about 582,878 (165)
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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Generalized twisted group rings [PDF]
Journal of Algebra, 2005 Let \(R\) be a Dedekind domain, and let \(G\) be an arbitrary group. The authors consider generalized group rings \(R*G\), twisted by a generalized 2-cocycle \(\alpha\colon G\times G\to R\setminus\{0\}\), i.e. with values not necessarily in \(R^\times\). Then \(H:=\{ x\in G\mid\alpha(x,x^{-1})\in R^\times\}\) is a subgroup of \(G\).
Nauwelaerts, E., Van Oystaeyen, Freddy
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Secure Group Communications Using Twisted Group Rings
Mathematics, 2022 In this paper we introduce a Group Key Management protocol following the idea of the classical protocol that extends the well-known Diffie–Hellman key agreement to a group of users. The protocol is defined in a non-commutative setting, more precisely, in
María Dolores Gómez Olvera +2 more
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Biology, 2023 Avian influenza is a severe viral infection that has the potential to cause human pandemics. In particular, chickens are susceptible to many highly pathogenic strains of the virus, resulting in significant losses. In contrast, ducks have been reported to
Hendrik Bertram +7 more
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Grothendieck Groups of Invariant Rings and of Group Rings
Journal of Algebra, 1994 Let \(G\) be a finite group acting as automorphisms of a (right) Noetherian ring \(S\), and \(R = S^ G\) be the fixed ring under this action. There is a Morita context linking the skew group ring \(T = S * G\) with \(R\), via the bimodules \(tT\) and \(Tt\) where \(t = \sum_{g \in G} g\). Suppose that the trace map \(\text{tr} : S \to R\) is surjective.
Brown, K.A., Lorenz, M.
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AIP Advances, 2022 Silicon is widely used in the semiconductor industry and has recently become very attractive as a lithium ion battery anode due to its high capacity. However, volume changes associated with repeated lithiation–delithiation cycles expose fresh silicon ...
Stéphane B. Olou’ou Guifo +3 more
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Maximal quotient rings of group rings [PDF]
Pacific Journal of Mathematics, 1974 The two which have received the greatest attention are theclassical (Ore) quotient ring and the maximal (Utumi) quotient ring.The classical quotient ring has a relatively straightforward description,but it is only defined for rings which satisfy the so-called Ore con-dition.
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On the non-existence of Abelian Moore Cayley graphs with excess one [PDF]
Discrete Mathematics Letters, 2021 Wei He
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Modules over group rings of groups with restrictions on the system of all proper subgroups [PDF]
International Journal of Group Theory, 2015 We consider the class M of R{modules where R is an associative ring. Let A be a module over a group ring RG, G be a group and let L(G) be the set of all proper subgroups of G. We suppose that if H 2 L(G) then A=CA(H) belongs to M. We study an RG{module A
Olga Dashkova
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On some modules over group rings of locally soluble groups with rank restrictions on subgroups [PDF]
Математичні Студії, 2011 The author studies an $f R$$G$-module $A$ such that $f R$is an integral domain, $G$ is a locally soluble group ofinfinite section $p$-rank (or infinite 0-rank), $C_{G}(A)=1$,$A/C_{A}(G)$ is not a~noetherian $f R$-module, and for everyproper subgroup $H ...
O. Yu. Dashkova
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