$SK_1$ for finite group rings: II.

The Auslander-Reiten Conjecture for Group Rings

This paper studies the vanishing of $Ext$ modules over group rings. Let $R$ be a commutative noetherian ring and $ga$ a group. We provide a criterion under which the vanishing of self extensions of a finitely generated $Rga$-module $M$ forces it to be projective. Using this result, it is shown that $Rga$ satisfies the Auslander-Reiten conjecture, whenever $R$ has finite global dimension and $ga...

group rings for communications

this is a survey of some recent applications of abstract algebra, and in particular group rings, to the `communications' areas.

Antisymmetric 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...

On Torsion Subgroups in Integral Group Rings of Finite Groups

On some subgroups of the multiplicative group of finite rings

Let S be a subset of Fq, the field of q elements and h ∈ Fq[x] a polynomial of degree d > 1 with no roots in S. Consider the group generated by the image of {x − s | s ∈ S} in the group of units of the ring Fq[x]/(h). In this paper we present a number of lower bounds for the size of this group. Our main motivation is an application to the recent polynomial time primality testing algorithm [AKS]...