On weakly clean rings

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 Anderson, D. D., Camillo, V. P. (2002). Commutative rings whose elements are a sum of a unit and idempotent. Commun. Algebra 30(7):3327–3336.Taylor & Francis Online], Web of Science ®] , Google Scholar]] and were extensively investigated by Ahn and Anderson 1 Ahn, M.-S., Anderson, D. D. (2006). Weakly clean rings and almost clean rings. Rocky Mountain J. Math. 36:783–798.Crossref], Web of Science ®] , Google Scholar]], 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.