Abstract. A ring R is called quasipolar if for every a ∈ R there exists p 2 = p ∈ R such that p ∈ comm 2 R (a), a + p ∈ U (R) and ap ∈ R qnil . The class of quasipolar rings lies properly between the class of strongly π-regular rings and the class of strongly clean rings. In this paper, we determine when a 2 × 2 matrix over a local ring is quasipolar. Necessary and sufficient conditions for a 2 × 2 matrix ring to be quasipolar are obtained.
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