Strongly clean triangular matrices over abelian rings

Authors

Alexander J. Diesl, Wellesley College
Thomas J. Dorsey, Center for Communication Research La Jolla
Wolf Iberkleid, Nova Southeastern UniversityFollow
Ramiro LaFuente-Rodriguez, D'Youville College
Warren Wm McGovern, Florida Atlantic University

Document Type

Article

Publication Date

11-1-2015

Publication Title

Journal of Pure and Applied Algebra

ISSN

00224049

Volume

219

Issue/No.

11

First Page

4889

Last Page

4906

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.

NSUWorks Citation

Diesl, Alexander J.; Dorsey, Thomas J.; Iberkleid, Wolf; LaFuente-Rodriguez, Ramiro; and McGovern, Warren Wm, "Strongly clean triangular matrices over abelian rings" (2015). Mathematics Faculty Articles. 332.
https://nsuworks.nova.edu/math_facarticles/332

DOI

10.1016/j.jpaa.2015.03.011