Strongly clean triangular matrices over abelian rings

Abstract

We investigate the problem of determining when a triangular matrix ring over a strongly clean ring is, itself, strongly clean. We prove that, if R is a commutative clean ring, then Tn(R) is strongly clean for every positive n. In the more general case that R is an abelian clean ring, we provide sufficient conditions which imply that Tn(R) is strongly clean. We end with a brief consideration of the non-abelian case.