Structure of Zhou Nil-clean Rings  

作　　者：Huanyin Chen Marian Sheibani 

机构地区：[1]Department of Mathematics, Hangzhou Normal University Hangzhou 311121, China [2]Women's University of Semnan (Farzanegan), Semnan, Iran

出　　处：《Algebra Colloquium》2018年第3期361-368,共8页代数集刊（英文版）

基　　金：The authors are grateful to the referee for his/her careful the paper, and for the invaluable comments which improve our presentation reading of author H.Y. Chen was supported by the Natural Science Foundation of Zhejiang （No. LY17A010018）, China. The first Province

摘　　要：A ring R is Zhou nil-clean if every element in R is the sum of two tripotents and a nilpotent that commute. Homomorphic images of Zhou nil-clean rings are explored. We prove that a ring R is Zhou nil-clean if and only if 30 ∈ R is nilpotent and R/30R is Zhou nil-clean, if and only if R/BM（R） is 5-potent and BM（R） is nil, if and only if J（R） is nil and R/J（R） is isomorphic to a Boolean ring, a Yaqub ring, a Bell ring or a direct product of such rings. By means of homomorphic images, we completely determine when the generalized matrix ring is Zhou nil-clean. We prove that the generalized matrix ring Mn（R; s） is Zhou nil-clean if and only if R is Zhou nil-clean and s ∈ J（R）.戒指 R 是周无干净如果在 R 的每个元素是变换的二 tripotents 和 nilpotent 的和。周的同构的图象无干净的戒指被探索。如果并且仅当 30 R 是 nilpotent ， R/30R 是周，我们证明戒指 R 是周无干净无干净如果(R)是无并且仅当 R/BM (R)是5有势力和 BM ，如果(R)对一枚布尔戒指同形并且仅当 J (R)是无和 R/J ，一枚 Yaqub 戒指，一枚贝尔戒指或如此的戒指的一个直接产品。借助于同构的图象，我们完全决定概括矩阵戒指什么时候是周无干净。我们证明概括矩阵包围 Mn (R；s ) 是周无干净如果并且仅当 R 是无干净的周和 s J (R) 。

关 键 词：tripotent NILPOTENT homomorphic images generalized matrix rings Zhou nil-clean rings 

分 类 号：O313.2[理学—一般力学与力学基础] TS934.3[理学—力学]