Certain Clean Decompositions for Matrices over Local Rings

Kurtulmaz Y., KÖSE H., Chen H.

Kyungpook Mathematical Journal, vol.63, no.4, pp.561-569, 2023 (ESCI, Scopus)

  • Publication Type: Article / Article
  • Volume: 63 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.5666/kmj.2023.63.4.561
  • Journal Name: Kyungpook Mathematical Journal
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, Academic Search Premier, zbMATH
  • Page Numbers: pp.561-569
  • Keywords: Local ring, Power-series, Strongly clean matrix, Strongly rad-clean matrix
  • Ankara University Affiliated: Yes

Abstract

Anelementae R is strongly rad-clean provided that there exists an idempotent e e R such that a — e e U(R), ae = ea and eae e J(eRe). In this article, we completely determine when a 2 x 2 matrix over a commutative local ring is strongly rad clean. An application to matrices over power-series is also given.