Group rings and semigroup rings over strong Mori domains. II. (Q1883038)

The concept of strong Mori domains was introduced by \textit{F. G. Wang} and \textit{R. L. McCasland} in [Commun. Algebra 25, 1285--1306 (1997; Zbl 0895.13010)] as a generalization of noetherian domains and Krull domains, which means an integral domain satisfying the ascending chain condition on \(w\)-ideals. The main aim of this paper is to characterize the condition under which the semigroup ring \(R[X;S]\) from an integral domain \(R\) and a torsion-free cancellative additive monoid \(S\) with quotient group \(G\) is a strong Mori semigroup. It is shown that \(R[X;S]\) is a strong Mori domain if and only if \(R\) is a strong Mori domain, \(S\) is a strong Mori semigroup and each nonzero element of \(G\) is of type \((0,0,\dots)\). [For Part I see J. Pure Appl. Algebra 163, No. 3, 301--318 (2001; Zbl 1094.13530).]