局部环及其扩张的强二和性质  

Strong 2-sum Property of Local Rings and Their Extensions

作　　者：唐高华[1] 吴严生[1] 张恒斌[1] 李玉[1] 

机构地区：[1]广西师范学院数学与统计科学学院,广西南宁530023

出　　处：《广西师范大学学报（自然科学版）》2016年第1期72-77,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11161006;11461010);广西科学研究与技术开发项目(桂科合1599005-2-13);广西高校科学技术研究项目(KY2015ZD075)

摘　　要：称环R的元有强二和环性质如果它可以写成该环中两个可换单位的和。如果环R的每个元都有强二和性质,则称R为强二和环。局部环是非常重要的环类,局部环及其扩张在环论、模论和同调代数等的研究中都有非常重要的地位。本文首先给出了局部环是强二和环的一个刻画,然后研究了局部环的幂级数扩张、平凡扩张和矩阵扩张等的强二和性。An element of a ring Ris called to have the strong 2-sum property if it is a sum of two units that commute with each other.And a ring Ris called a strong 2-sum ring if every element of Rhas the strong 2-sum property.Local ring is a very important class of rings.Local rings and their extensions are very important in the research of ring theory,module theory and homological algebra.In this article,a characterization of a local ring to be a strong 2-sum ring is given.Then,the strong 2-sum property of local rings and their power series extension,trivial extension and matrix extension are studied.

关 键 词：2-good环 强二和环 局部环 环扩张 

分 类 号：O153.3[理学—数学]