Journal of Jishou University(Natural Sciences Edition)

Previous Articles     Next Articles

Semiprime Modules and Reduced Modules

LI Dongfang,LI Qisheng   

  1. (College of Mathematics and Statics,Jishou University,Jishou 416000,Hunan China)
  • Online:2016-03-25 Published:2016-05-11

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

WeChat e-book chaoxing Mobile QQ