Strong J-Cleanness of Formal Matrix Rings

2013/08/19 by Gurgun, Orhan, Halıcıoglu, Sait, Harmanci, Abdullah
Mathematics · #16S50 #16S70 #16U99 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16S50 #msc:16S70 #msc:16U99

paper · pdf · doi:10.48550/arxiv.1308.4105

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.

Related

• The strong P-cleanness over rings
• Strong cleanness of the 2× 2 matrix ring over a general local ring
• On Perfectly Clean Rings
• Very clean matrices over local rings
• Strongly J-clean matrices over 2-projective-free rings