Semigroup rings which are strongly nil-clean

Abstract

Strongly nil-cleanness and uniquely nil-cleanness are two important clean properties of rings. The aim of this paper is to answer when a semigroup ring is strongly or uniquely nil-clean. We obtain conditions on a coefficient ring together with conditions on a semigroup that completely characterize when the corresponding semigroup ring is strongly nil-clean. Moreover, when the coefficient ring is an integral domain, we characterize when the corresponding semigroup ring is uniquely nil-clean.