(untitled) (Communications in Mathematical Research, 2021)
Pseudopolar rings are closely related to strongly π-regular rings, uniquely strongly clean rings and semiregular rings. In this paper, we investigate pseudopolarity of generalized matrix rings K_s(R) over a local ring R. We determine the conditions under which elements of K_s(R) are pseudopolar. Assume that R is a local ring. It is shown that A∈ K_s(R) is pseudopolar if and only if A is invertible or A^2 ∈ J(K_s(R)) or A is similar to a diagonal matrix bmatrix u & 0 0 & j bmatrix, where l_u −r_j and l_j −r_u are injective and u ∈ U(R) and j ∈ J(R). Furthermore, several equivalent conditions for K_s(R) over a local ring R to be pseudopolar are obtained.