談擬入射模

SOME REMARKS ON QUASI-INJECTIVE MODULES

本文主要在討論擬入射模與其扭元素之集合間的關係。

The purpose of this paper is to give some supplementary remarks of the previous work [1] by the author. The nota-tions and terminologies are referred to [1]. We shall prove that for any quasi-injective R-module M， (i) if R is not a domain， then either TR(M)(TR(M))=M or TR(M)=(TR(M)) C (TR(M))=M; (ii) if R is a domain， then either TR(M)((TR(M))=M or TR(M)=(R(M)) is a proper direct summand of M.