Strong $J$-Cleanness of Formal Matrix Rings

Abstract

An element a of a ring R is called strongly J-clean provided that there exists an idempotent e ∈ R such that a − e ∈ J(R) and ae = ea. A ring R is strongly J-clean in case every element in R is strongly J-clean. In this paper, we investigate strong J-cleanness of M2(R; s) for a local ring R and s ∈ R. We determine the conditions under which elements of M2(R; s) are strongly J-clean.