## Abstract

An element a of a ring R is called quasipolar provided that there exists an idempotent p ∈ R such that p ∈ comm^{2}(a), a + p ∈ U (R) and ap ∈ B^{qnil}. A ring R is quasipolar in case every element in R is quasipolar. In this paper, we determine conditions under which subrings of 3 x 3 matrix rings over local rings are quasipolar. Namely, if R. is a bleached local ring, then we prove that T_{3} (R) is quasipolar if and only if R is uniquely bleached. Furthermore, it is shown that T_{n}(R) is quasipolar if and only if T_{n}(R[[x]]) is quasipolar for any positive integer

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