Technique of semigroup ring theory: Regular semigroup rings (Q1807489)

Let \(S\) be a semigroup and \(G\) a subgroup of \(S\). Let \(R\) be a ring (perhaps, without unity) and \(R'\) a subring of \(R\). The author gives connections between properties of the group ring \(RG\) and the semigroup ring \(RS\), and also the semigroup rings \(RS\) and \(R'S\). Some equivalent conditions for a group ring \(RG\) to be regular are given. Properties that are weaker or stronger than regularity are also considered.