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

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.

5 pages, 1 figure, translation from the French original Renault, Guy. "Sur les anneaux de groupes." CR Acad. Sci. Paris Sér. AB 273 (1971): A84-A87