强π nil clean环（英文）

On Strongly π Nil Clean Rings

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.