Strong J-cleanness of formal matrix rings

Gurgun O., HALICIOĞLU S., Harmanci A.

Advanced Studies in Contemporary Mathematics (Kyungshang), vol.24, no.4, pp.483-498, 2014 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 4
  • Publication Date: 2014
  • Journal Name: Advanced Studies in Contemporary Mathematics (Kyungshang)
  • Journal Indexes: Scopus, MathSciNet, zbMATH
  • Page Numbers: pp.483-498
  • Keywords: Formal matrix ring, Local ring, Strongly clean, Strongly J-clean, Strongly nil clean
  • Ankara University Affiliated: Yes

Abstract

An element a of a ring R is called strongly J-clean provided that there exists an idempotent e ∈ R such that a - e ∈ J(R) and ae = ea. A ring R, is strongly J-clean in case every element in R is strongly J-clean. In this paper, we investigate strong J-cleanness of M2(R;s) for a local ring R and s ∈ R. We determine the conditions under which elements of M2(R; s) are strongly J-clean.