Cohn localization of finite group rings

Localization at prime ideals in bounded rings

In this paper we investigate the sufficiency criteria which guarantee the classical localization of a bounded ring at its prime ideals.

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]...

Primitive central idempotents of finite group rings of symmetric groups

Let p be a prime. We denote by Sn the symmetric group of degree n, by An the alternating group of degree n and by Fp the field with p elements. An important concept of modular representation theory of a finite group G is the notion of a block. The blocks are in one-to-one correspondence with block idempotents, which are the primitive central idempotents of the group ring FqG, where q is a prime...

On Torsion Subgroups in Integral Group Rings of Finite Groups

Maximal Quotient Rings and Essential Right Ideals in Group Rings of Locally Finite Groups

MAXIMAL QUOTIENT RINGS AND ESSENTIAL RIGHT IDEALS IN GROUP RINGS OF LOCALLY FINITE GROUPS Theorem . zero . FERRAN CEDÓ * AND BRIAN HARTLEY Dedicated to the memory of Pere Menal Let k be a commutative field . Let G be a locally finite group without elements of order p in case char k = p > 0 . In this paper it is proved that the type I. part of the maximal right quotient ring of the group algebgr...