Strongly clean triangular matrix rings with endomorphisms

Chen H., KÖSE H., Kurtulmaz Y.

Bulletin of the Iranian Mathematical Society, cilt.41, sa.6, ss.1365-1374, 2015 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 6
  • Basım Tarihi: 2015
  • Dergi Adı: Bulletin of the Iranian Mathematical Society
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1365-1374
  • Anahtar Kelimeler: Local rings, Skew triangular matrix rings, Strongly clean rings
  • Ankara Üniversitesi Adresli: Evet

Özet

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 aϵ 1+J(R); b ϵ 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 ϵ U(R); b ϵ J(R). The necessary condition for T3(R; σ) to be strongly clean is also obtained.