On commutative rings over which the singular submodule is a direct summand for every module

Vasily Cateforis and Francis Louis Sandomierski

Vol. 31 (1969), No. 2, 289–292

DOI: 10.2140/pjm.1969.31.289

Abstract

A commutative ring R with 1 over which the singular submodule is a direct summand for every module, is a semihereditary ring with finitely many large ideals. A commutative semi-simple (with d.c.c.) ring is characterized by the property that every semi-simple module is injective.

Mathematical Subject Classification

Primary: 13.50

Milestones

Received: 18 February 1969

Published: 1 November 1969