J-正则模与J-正则环  

J-Regular Modules and Rings

作　　者：向跃明 万欣 XIANG Yue-ming;WAN Xin(School of Mathematics and Computational Science,Huaihua University,Huaihua,Hunan 418008)

机构地区：[1]怀化学院数学与计算科学学院,湖南怀化418000

出　　处：《怀化学院学报》2021年第5期1-5,共5页Journal of Huaihua University

基　　金：湖南省自然科学基金项目“范畴代数的同调理论研究”(2021JJ30536).

摘　　要：作为正则性的推广,沈亮引入了J-正则环,一些已知的结论得到了推广.引入了J-正则模,包括半正则模和半局部模,给出了J-正则模和J-正则环一些特征,进而,考虑了J-正则环的一些扩张.As a generalization of regularity,Shen liang introduced the J-regularity of rings and some known results have been disseminated.In the present paper,we develop a class of J-regular modules which contain all semiregular modules and semilocal modules.Some characterizations of J-regular modules and J-regular rings are given.Furthermore,several extensions of J-regular rings are also considered.

关 键 词：J-正则模 J-正则环 环扩张 

分 类 号：O153.3[理学—数学]