Uniquely strongly clean triangular matrices

Chen H., Gurgun O., KÖSE H.

TURKISH JOURNAL OF MATHEMATICS, cilt.39, sa.5, ss.645-649, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 5
  • Basım Tarihi: 2015
  • Doi Numarası: 10.3906/mat-1408-13
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.645-649
  • Anahtar Kelimeler: Uniquely strongly clean ring, uniquely bleached ring, triangular matrix ring, RINGS, ELEMENTS, IDEMPOTENT, UNIT, SUM
  • Ankara Üniversitesi Adresli: Evet

Özet

A ring R is uniquely (strongly) clean provided that for any a is an element of R there exists a unique idempotent e is an element of R (e is an element of comm(a)) such that a e is an element of U(R). We prove, in this note, that a ring R is uniquely clean and uniquely bleached if and only if R is abelian, T-n(R) is uniquely strongly clean for all n >= 1, i.e. every n x n triangular matrix over R is uniquely strongly clean, if and only if R is abelian, and T-n(R) is uniquely strongly clean for some n >= 1. In the commutative case, more explicit results are obtained.