关键词： 约化模, 完全半素模, 经典完全半素模, 对称模, 正则模

Abstract:

The properties of several classes of zero-insertive modules and semi-prime modules are discussed. It is proved that the flat modules over a classical completely semi-prime (respectively zero-insertive) ring is classical completely semi-prime (respectively zero-insertive).Several characterizations of reduced modules and left duo-rings are obtained.Let M be a left R-module，it is shown that if M is symmetric then M/Z(M) is reduced，where Z(M) is the singular submodule of M；if M is  regular then M is reduced if and only if it is Abelian.

Key words: reduced modules, completely semi-prime modules, classical completely semi-prime modules, symmetric modules, regular modules