Semigroup rings with certain finiteness conditions (Q1807497)

This is a survey of results on semigroup rings \(R[S]\) satisfying certain classical chain conditions. The topics considered include local and semilocal, Artinian, perfect and semiprimary, algebraically compact, self-injective and Noetherian rings. Many of the results presented are extensions of results known for semigroup algebras \(K[S]\) over a field \(K\) [see the monograph ``Semigroup Algebras'' (Marcel Dekker, 1991; Zbl 0725.16001) by the reviewer] to the case of arbitrary coefficient rings \(R\). -- There are essential gaps in the bibliography.