Results 31 to 40 of about 222,859 (215)
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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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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Rings Graded By a Generalized Group
Topological Algebra and its Applications, 2014 The aim of this paper is to consider the ringswhich can be graded by completely simple semigroups.We show that each G-graded ring has an orthonormal basis, where G is a completely simple semigroup. Weprove that if I is a complete homogeneous ideal of a G-
Fatehi Farzad, Molaei Mohammad Reza
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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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Group Action on the Set of Nonunits in Rings
Journal of Mathematics, 2023 Let R be a ring, G be the group of all units of R, and X=R−G∪0. In this paper, we investigate avxx∈X=oxx∈X for a ring R, where avx is the set of all vertices of the zero-divisor graph of R adjacent to x.
Eman S. Almotairi +2 more
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Paraunitary matrices and group rings [PDF]
International Journal of Group Theory, 2014 Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structuresare presented. These include techniques for designing non-separable multidimensional paraunitary matrices.
Barry Hurley, Ted Hurley
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Skew group rings which are Galois
International Journal of Mathematics and Mathematical Sciences, 2000 Let S*G be a skew group ring of a finite group G over a ring S. It is shown that if S*G is an G′-Galois extension of (S*G)G′, where G′ is the inner automorphism group of S*G induced by the elements in G, then S is a G-Galois extension of SG.
George Szeto, Lianyong Xue
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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 structure of artinian-by-(finite rank) modules over generalized soluble groups
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika, 2014 Let R be a ring and G a group. An R-module A is said to be artinian-by-(finite rank), if $\mathrm{Tor}_R(A)$ is artinian and $A/\mathrm{Tor}_R(A)$ has finite R-rank.
V.A. Chupordia
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