Quasipolar matrix rings over local rings
Bull. Korean Math. Soc. 2014 Vol. 51, No. 3, 813-822
https://doi.org/10.4134/BKMS.2014.51.3.813
Published online May 31, 2014
Jian Cui and Xiaobin Yin
Anhui Normal University, Anhui Normal University
Abstract : A ring $R$ is called quasipolar if for every $a\in R$ there exists $p^2=p\in R$ such that $p\in{\rm comm}^2_R(a)$, $a+p\in U(R)$ and $ap\in R^{\rm qnil}.$ The class of quasipolar rings lies properly between the class of strongly $\pi$-regular rings and the class of strongly clean rings. In this paper, we determine when a $2\times 2$ matrix over a local ring is quasipolar. Necessary and sufficient conditions for a $2\times 2$ matrix ring to be quasipolar are obtained.
Keywords : quasipolar ring, matrix ring, strongly clean ring, local ring
MSC numbers : 16U99
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