拟fine环和2-fine环  

Quasi-fine and 2-fine Rings

作　　者：崔雨茹 崔建 程杨 CUI Yuru;CUI Jian;CHENG Yang(School of Mathematics and Statistics,Anhui Normal University,Wuhu,Anhui,241002,P.R.China)

机构地区：[1]安徽师范大学数学与统计学院,安徽芜湖241002

出　　处：《数学进展》2024年第1期125-132,共8页Advances in Mathematics（China）

基　　金：Supported by the Key Laboratory of Financial Mathematics of Fujian Province University(Putian University)(No.JR202203);NSF of Anhui Province(No.2008085MA06);the project of Anhui Education Committee(No.gxyqZD2019009)。

摘　　要：称环R是fine环,如果R中每个非零元素均可以表示为一个可逆元与一个幂零元之和.Fine环的概念由Cǎlugǎreanu和Lam在[J.Algebr Appl.,2016,15(9):1650173,18 pp.]中给出,fine环和单环密切相关.本文研究如下两类环:每个非幂零元素均可表示为一个可逆元与一个幂等元之和的环以及每个元素均可表示为一个可逆元与两个幂零元之和的环.A ring R is fine if every nonzero element of R is the sum of a unit and a nilpotent.The notion of fine rings is closely related to simple rings,which was introduced by Calugareanu and Lam in[J.Algebra Appl.,2016,15(9):1650173,18 pp.].In this paper,we study rings in which every non-nilpotent element is the sum of a unit and a nilpotent,and rings in which every element is the sum of a unit and two nilpotents.

关 键 词：fine环 拟fine环 2-fine环 矩阵环 

分 类 号：O153.3[理学—数学]