Strongly j-clean skew triangular matrix rings

Abstract

Let R be an arbitrary ring with identity. An element a 2 R is strongly J-clean if there exist an idempotent e 2 R and element w 2 J(R) such that a = e + w and ew = ew. A ring R is strongly J-clean in case every element in R is strongly J-clean. In this note, we investigate the strong J-cleanness of the skew triangular matrix ring Tn(R, ) over a local ring R, where is an endomorphism of R and n = 2, 3, 4.