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数学进展 - 2018, Vol. 47(2): 189-200
研究论文
强${\pi}$ nil clean 环
On Strongly ${\pi}$ Nil Clean Rings

欧阳伦群1,周琼1,刘金旺1,向跃明2
OUYANG Lunqun1,*, ZHOU Qiong1, LIU Jinwang1, XIANG Yueming2

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
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. China

收稿日期: 2016-06-23
出版日期: 2018-05-16
2018, Vol. 47(2): 189-200
DOI: 10.11845/sxjz.2016084b


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摘要 作为强nil clean 环的推广, 本文引进了强$\pi$ nil clean 环的新概念. 首先探讨了强$\pi$ nil clean 环的基本性质并构造出强$\pi$ nil clean 环的典型例子, 接着用一些特殊多项式的分解来对强$\pi$ nil 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.
关键词 强$\pi$nilclean环特征多项式投射自由环    
Abstract:We in this note introduce a new concept, so-called strongly $\pi$ nil clean ring, that is a generalization of strongly nil clean rings. We first observe the basic properties of strongly $\pi$ nil clean rings, and construct typical examples. We next characterize the strongly $\pi$ 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.
Key wordsstrongly $\pi$ nil clean ring    characteristic polynomial    projective-free ring
PACS:  O153.3  
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