Year: 2015
Author: Xiaobin Yin, Dou Wan
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 211–221
Abstract
Pseudopolar rings are closely related to strongly $π$-regular rings, uniquely strongly clean rings and semiregular rings. In this paper, we investigate pseudopolarity of generalized matrix rings $K_s(R)$ over a local ring $R$. We determine the conditions under which elements of $K_s(R)$ are pseudopolar. Assume that $R$ is a local ring. It is shown that $\boldsymbol{A}∈ K_s(R)$ is pseudopolar if and only if $\boldsymbol{A}$ is invertible or $\boldsymbol{A}^2 ∈ J(K_s(R))$ or $\boldsymbol{A}$ is similar to a diagonal matrix $\begin{bmatrix} u & 0 \\ 0 & j \end{bmatrix}$, where $l_u −r_j$ and $l_j −r_u$ are injective and $u ∈ U(R)$ and $j ∈ J(R)$. Furthermore, several equivalent conditions for $K_s(R)$ over a local ring $R$ to be pseudopolar are obtained.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2015.03.03
Communications in Mathematical Research , Vol. 31 (2015), Iss. 3 : pp. 211–221
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 11
Keywords: pseudopolar ring local ring generalized matrix ring.