Strongly clean triangular matrices over abelian rings

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 T-n(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 T-n(R) is strongly clean. We end with a brief consideration of the non-abelian case. (C) 2015 Elsevier B.V. All rights reserved.