Strongly clean matrices over power series


CHEN H., KÖSE H., KURTULMAZ Y.

Kyungpook Mathematical Journal, vol.56, no.2, pp.387-396, 2016 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 56 Issue: 2
  • Publication Date: 2016
  • Doi Number: 10.5666/kmj.2016.56.2.387
  • Journal Name: Kyungpook Mathematical Journal
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.387-396
  • Ankara University Affiliated: No

Abstract

An n x n matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let A(x) is an element of M-n (R[[x]]). We prove, in this note, that A(x) is an element of M-n (R[[x]]) is strongly clean if and only if A(0) is an element of M-n (R) is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.