منابع مشابه
Infinite groups and primitivity of their group rings
we focus on a local property which is often satisfied by groups with non-abelian free subgroups: (∗) For each subset M of G consisting of finite number of elements not equal to 1, there exist three distinct elements a, b, c in G such that whenever xi ∈ {a, b, c} and (x−1 1 g1x1) · · · (x−1 m gmxm) = 1 for some gi ∈ M , xi = xi+1 for some i. We can see that the group algebra KG of a group G over...
متن کاملAntisymmetric Elements in Group Rings Ii
Let R be a commutative ring, G a group and RG its group ring. Let φ : RG → RG denote the R-linear extension of an involution φ defined on G. An element x in RG is said to be φantisymmetric if φ(x) = −x. A characterization is given of when the φ-antisymmetric elements of RG commute. This is a completion of earlier work. keywords: Involution; group ring; antisymmetric elements. keywords: 2000 Mat...
متن کاملStably Just Infinite Rings
We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite provided that the ring is either right noetherian (4.2) or countably generated over a large field (6.4). We give examples to show that, over countable fields...
متن کاملCOTORSION DIMENSIONS OVER GROUP RINGS
Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.
متن کاملMultiplicative Jordan Decomposition in Group Rings of 3-groups, Ii
In this paper, we complete the classification of those finite 3groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that Z[G] satisfies MJD. In the nonabelian case, we show that Z[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.
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ژورنال
عنوان ژورنال: Bulletin of the Faculty of Science, Ibaraki University. Series A, Mathematics
سال: 1976
ISSN: 1883-4345,0579-3068
DOI: 10.5036/bfsiu1968.8.43