半素模与约化模  

Semiprime Modules and Reduced Modules

作　　者：李东方[1] 黎奇升[1] 

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000

出　　处：《吉首大学学报（自然科学版）》2016年第2期6-10,共5页Journal of Jishou University(Natural Sciences Edition)

基　　金：湖南省研究生创新科研基金资助项目(CX2015B434)

摘　　要：讨论了几种半素模和零插入模的性质,证明了经典完全半素环上的平坦模是经典完全半素的,零插入环上的平坦模是零插入的.给出了约化模和左duo-环的新的等价条件.证明了若模M是对称的,则M/Z(M)是约化的,其中Z(M)为M的奇异子模;若M是正则模,则M是约化的当且仅当它是Abel模.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;f M is regular then M is reduced if and only if it is Abelian.

关 键 词：约化模 完全半素模 经典完全半素模 对称模 正则模 

分 类 号：O153.1[理学—数学]