2013/06/11 by H. Chen, Chen, H., Handan Köse +5
Computer Science · Mathematics · #Advanced Algebra and Logic #Advanced Topics in Algebra #Rings, Modules, and Algebras #math.RA #msc:16D70 #msc:16E50
paper · pdf · doi:10.48550/arxiv.1306.2440
arxiv created 2013/06/11 · arxiv updated 2013/06/12
A ring R is strongly clean provided that every element in R is the sum of an idempotent and a unit that commutate. Let Tn(R,σ) be the skew triangular matrix ring over a local ring R where σ is an endomorphism of R. We show that T2(R,σ) is strongly clean if and only if for any a∈ 1+J(R), b∈ J(R), la-rσ(b): R→ R is surjective. Further, T3(R,σ) is strongly clean if la-rσ(b), la-rσ2(b) and lb-rσ(a) are surjective for any a∈ U(R),b∈ J(R). The necessary condition for T3(R,σ) to be strongly clean is also obtained.