正则模  

Regular modules

作　　者：王利民[1] 雷蕾[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2011年第1期23-25,共3页Journal of Northwest Normal University(Natural Science)

摘　　要：引入一种新的模类,即正则模,讨论了正则模中的正则元和正则对的性质,给出了正则模中的正则元与幂等元的关系,并得到了模为正则模的充分必要条件的刻画.同时,对正则模的投射性、挠自由性与可除性等进行了研究.最后,给出了内射正则模的一些性质.The concept of regular module is introduced,and some properties of regular elements and regular pairs are discussed,the relations of regular elements and idempotent elements are given,then some equivalent characterizations of regular modules are obtained.In addition,the projectivity,torsionfreeness,divisibility of regular modules are studied.Finally,some properties of injective regular modules are described.

关 键 词：正则元 正则模 正则对 正则左理想 挠自由模 

分 类 号：O154[理学—数学]