On weakly clean rings

Kosan T., Sahinkaya S., Zhou Y.

COMMUNICATIONS IN ALGEBRA, vol.45, no.8, pp.3494-3502, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 45 Issue: 8
  • Publication Date: 2017
  • Doi Number: 10.1080/00927872.2016.1237640
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3494-3502
  • Keywords: 2-Good ring, clean ring, uniquely clean ring, weakly clean ring, ELEMENTS, SUM
  • Gazi University Affiliated: No


A ring is called clean if every element is a sum of a unit and an idempotent, while a ring is said to be weakly clean if every element is either a sum or a difference of a unit and an idempotent. Commutative weakly clean rings were first discussed by Anderson and Camillo [2] and were extensively investigated by Ahn and Anderson [1], motivated by the work on clean rings. In this paper, weakly clean rings are further discussed with an emphasis on their relations with clean rings. This work shows new interesting connections between weakly clean rings and clean rings.