The exchange property and direct sums of indecomposable injective modules

Kunio Yamagata

Vol. 55 (1974), No. 1, 301–317

DOI: 10.2140/pjm.1974.55.301

Abstract

This paper contains two main results. The first gives a necessary and sufficient condition for a direct sum of indecomposable injective modules to have the exchange property. It is seen that the class of these modules satisfying the condition is a new one of modules having the exchange property. The second gives a necessary and sufficient condition on a ring for all direct sums of indecomposable injective modules to have the exchange property.

Mathematical Subject Classification

Primary: 16A52

Milestones

Received: 17 July 1973

Revised: 9 April 1974

Published: 1 November 1974