Turkish Journal of Mathematics
Article Title
DOI
10.3906/mat-1802-10
Abstract
We are concerned about various strongly clean properties of a kind of matrix subrings $L_{(s)}(R)$ over a local ring $R$. Let $R$ be a local ring, and let $s\in C(R)$. We prove that $A\in L_{(s)}(R)$ is strongly clean if and only if $A$ or $I_2-A$ is invertible, or $A$ is similar to a diagonal matrix in $L_{(s)}(R)$. Furthermore, we prove that $A\in L_{(s)}(R)$ is quasipolar if and only if $A\in GL_2(R)$ or $A\in L_{(s)}(R)^{qnil}$, or $A$ is similar to a diagonal matrix $\left( \begin{array}{cc} \lambda&0\\ 0&\mu \end{array} \right)$ in $L_{(s)}(R)$, where $\lambda\in J(R)$, $\mu\in U(R)$ or $\lambda\in U(R)$, $\mu\in J(R)$, and $l_{\mu}-r_{\lambda}$, $l_{\lambda}-r_{\mu}$ are injective. Pseudopolarity of such matrix subrings is also obtained.
First Page
2296
Last Page
2303
Recommended Citation
ÇALCI, TUĞÇE PEKACAR and CHEN, HUANYIN
(2018)
"Certain strongly clean matrices over local rings,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 16.
https://doi.org/10.3906/mat-1802-10
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/16
