1
Department of Mathematics, Hangzhou Normal University, Hangzhou 310034, China
2
Department of Mathematics, Ahi Evran University, Kirsehir, Turkey
3
Department of Mathematics, Bilkent University, Ankara, Turkey
Abstract
A ring $R$ is strongly clean provided that every element in $R$ is the sum of an idempotent and a unit that commutate. Let $T_n(R,\sigma)$ be the skew triangular matrix ring over a local ring $R$ where $\sigma$ is an endomorphism of $R$. We show that $T_2(R,\sigma)$ is strongly clean if and only if for any $a\in 1+J(R), b\in J(R)$, $l_a-r_{\sigma(b)}: R\to R$ is surjective. Further, $T_3(R,\sigma)$ is strongly clean if $l_{a}-r_{\sigma(b)}, l_{a}-r_{\sigma^2(b)}$ and $l_{b}-r_{\sigma(a)}$ are surjective for any $a\in U(R),b\in J(R)$. The necessary condition for $T_3(R,\sigma)$ to be strongly clean is also obtained.
Chen, H., Kose, H., & Kurtulmaz, Y. (2015). Strongly clean triangular matrix rings with endomorphisms. Bulletin of the Iranian Mathematical Society, 41(6), 1365-1374.
MLA
Chen, H., Kose, H., & Kurtulmaz, Y. "Strongly clean triangular matrix rings with endomorphisms", Bulletin of the Iranian Mathematical Society, 41, 6, 2015, 1365-1374.
HARVARD
Chen H., Kose H., Kurtulmaz Y. (2015). 'Strongly clean triangular matrix rings with endomorphisms', Bulletin of the Iranian Mathematical Society, 41(6), pp. 1365-1374.
CHICAGO
H. Chen, H. Kose & Y. Kurtulmaz, "Strongly clean triangular matrix rings with endomorphisms," Bulletin of the Iranian Mathematical Society, 41 6 (2015): 1365-1374,
VANCOUVER
Chen H., Kose H., Kurtulmaz Y. Strongly clean triangular matrix rings with endomorphisms. BIMS. 2015;41(6):1365-1374.
