THE ENDOMORPHISM RING OF A NONSINGULAR RETRACTABLE MODULE

Abstract

Let RM be a nonsingular retractable module with endomorphism ring E. It is proved that E is left quasi-continuous if and only if M is quasicontinuous, E is left continuous and regular if and only if M is continuous, and EE has the absolute direct summand (ads) property if and only if M is an ads module. Some properties of left complements in E are also transferred to M.