Cleanness of overrings of polynomial rings

Authors

Department of Mathematics, Al al-Bayt University, Mafraq, Jordan

10.1016/j.joems.2014.08.003

Abstract

Let R be a commutative ring with identity. R is called clean (respectively, almost clean) if
every element in R is a sum of an idempotent and a unit (respectively, a regular element). In this
paper, we clarify conditions under which the two overrings RðxÞ and Rhxi of the ring of polynomials
R½x are (almost) clean rings.