On group rings: a translation of "Sur les anneaux de groupes" by Guy Renault

TL;DR

This paper characterizes when group rings are local, semi-local, or left perfect, building on recent work to complete earlier results on self-injective group rings.

Contribution

It provides a comprehensive characterization of group rings' properties, extending previous research with new results on self-injective group rings.

Findings

Characterization of local and semi-local group rings

Conditions for group rings to be left perfect

Completion of earlier results on self-injective group rings

Abstract

(Translation from the original French:) We characterize the rings $A$ and groups $G$ for which the group rings $A [G]$ are local, semi-local, or left perfect. The recent work of M. P. Malliavin and J. L. Pascaud permits the completion of results of [an earlier publication by the author] on self-injective group rings.