TY - JOUR
T1 - Pseudopolarity of Generalized Matrix Rings over a Local Ring
AU - Yin , Xiaobin
AU - Wan , Dou
JO - Communications in Mathematical Research 
VL - 3
SP - 211
EP - 221
PY - 2021
DA - 2021/05
SN - 31
DO - http://doi.org/10.13447/j.1674-5647.2015.03.03
UR - https://global-sci.org/intro/article_detail/cmr/18922.html
KW - pseudopolar ring, local ring, generalized matrix ring.
AB - <p style="text-align: justify;">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&nbsp;$\begin{bmatrix} u &amp; 0 \\ 0 &amp; j \end{bmatrix}$, 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.</p>