STRONGLY PRIME GROUP RINGS

1 January 1979

journal article
research article
Published by Taylor & Francis in Quaestiones Mathematicae

Vol. 3 (4) , 241-247
https://doi.org/10.1080/16073606.1979.9631576

Abstract

A ring R is (right) strongly prime (SP) if every nonzero two sided ideal contains a finite set whose right annihilator is zero, SP rings have been studied by Handelman and Lawrence who raised the problem of characterizing SP group algebras. They showed that if R is SP and G is torsion free Abelian, then the group ring RG is SP. The aim of this note is to determine some more group rings which are SP. For a ring R we also define the strongly prime radical s(R). We then show that s(R)G = s(W) for certain classes of groups.

Keywords

20C05

This publication has 3 references indexed in Scilit:

Maximal quotient rings of prime group algebras. II Uniform right ideals
Journal of the Australian Mathematical Society, 1977
Strongly prime rings
Transactions of the American Mathematical Society, 1975
Absolutely torsion-free rings
Pacific Journal of Mathematics, 1973