Almost quasi clean rings

ÖZDİN T.

TURKISH JOURNAL OF MATHEMATICS, cilt.45, sa.2, ss.961-970, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.3906/mat-2012-77
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.961-970
  • Erzincan Binali Yıldırım Üniversitesi Adresli: Evet

Özet

The element q of a ring R is called quasi-idempotent element if q(2) = uq for some central unit u of R, or equivalently q = ue, where u is a central unit and e is an idempotent of R. In this paper, we define that the ring R is almost quasi-clean if each element of R is the sum of a regular element and a quasi-idempotent element. Several properties of almost-quasi clean rings are investigated. We prove that every quasi-continuous and nonsingular ring is almost quasi-clean. Finally, it is determined that the conditions under which the idealization of an R-module M is almost quasi clean.