QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS

Title & Authors
QUASIPOLAR MATRIX RINGS OVER LOCAL RINGS
Cui, Jian; Yin, Xiaobin;

Abstract
A ring R is called quasipolar if for every a 2 R there exists $\small{p^2=p{\in}R}$ such that $\small{p{\in}comm^2{_R}(a)}$, $\small{ a+p{\in}U(R)}$ and $\small{ap{\in}R^{qnil}}$. The class of quasipolar rings lies properly between the class of strongly $\small{{\pi}}$-regular rings and the class of strongly clean rings. In this paper, we determine when a $\small{2{\times}2}$ matrix over a local ring is quasipolar. Necessary and sufficient conditions for a $\small{2{\times}2}$ matrix ring to be quasipolar are obtained.
Keywords
quasipolar ring;matrix ring;strongly clean ring;local ring;
Language
English
Cited by
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