On weakly nil-clean rings  

作　　者：M. Tamer KOSAN Yiqiang ZHOU 

机构地区：[1]Department of Mathematics, Gebze Technical University, Gebze/Kocaeli, Turkey [2]Department of Mathematics and Statistics, Memorial University of Newfoundland,St. John's, NL A1C 5S7, Canada

出　　处：《Frontiers of Mathematics in China》2016年第4期949-955,共7页中国高等学校学术文摘·数学（英文）

摘　　要：We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.We obtain the structure of the rings in which every element is either a sum or a difference of a nilpotent and an idempotent that commute. This extends the structure theorems of a commutative weakly nil-clean ring, of an abelian weakly nil-clean ring, and of a strongly nil-clean ring. As applications, this result is used to determine the 2-primal rings R such that the matrix ring Mn（R） is weakly nil-clean, and to show that the endomorphism ring EndD（V） over a vector space VD is weakly nil-clean if and only if it is nil-clean or dim（V） = 1 with D Z3.

关 键 词：Nil-clean ring strongly nil-clean ring weakly nil-clean ring matrix ring endomorphism ring of a vector space 2-primal ring 

分 类 号：O189.3[理学—数学] O152.7[理学—基础数学]