强π nil clean环（英文）  

On Strongly π Nil Clean Rings

作　　者：欧阳伦群 周琼[1] 刘金旺 向跃明[2] OUYANG Lunqun1, ZHOU Qiong1, LIU Jinwang1, XIANG Yueming2(1. Department of Mathematics, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, P. R. China; 2. Department of Mathematics and Applied Mathematics, Huaihua University, Huaihua, Hunan, 418000, P. R. Chin)

机构地区：[1]湖南科技大学数学系,湘潭湖南411201 [2]怀化学院数学与应用数学系,怀化湖南418000

出　　处：《数学进展》2018年第2期189-200,共12页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11471108);Natural Science Foundation of Hunan Province(Nos.2015JJ2051,2016JJ2050);Scientific Research Foundation of Hunan Provincial Education Department(No.12B101);the Teaching Reform Foundation of Hunan Province(No.G21316)

摘　　要：作为强nil clean环的推广,本文引进了强πnil clean环的新概念.首先探讨了强πnil clean环的基本性质并构造出强πnil clean环的典型例子,接着用一些特殊多项式的分解来对强πnil clean矩阵进行刻画,从而将一些熟知的强nil clean环的性质推广到更一般的情况.We in this note introduce a new concept, so-called strongly π nil clean ring, that is a generalization of strongly nil clean rings. We first observe the basic properties of strongly π nil clean rings, and construct typical examples. We next characterize the strongly π nil cleanness of matrices in terms of the factorization of some special polynomials. As a consequence, several known results relating to strongly nil clean rings are extended to a more general setting.

关 键 词：强π NIL CLEAN环 特征多项式 投射自由环 

分 类 号：O153.3[理学—数学]