On a question posed by Huckaba-Papick. IV (Q2747338)

The paper under review is an addendum to the author's previous part III of this paper [\textit{R. Matsuda}, Far East J. Math. Sci. 2, No. 5, 695-701 (2000; Zbl 0977.13008)]. Let \(A\) be a (commutative) Marot ring with property (A), that is, every regular ideal of \(A\) is generated by regular elements of \(A\) and for each regular element \(f\) of the polynomial ring \(A[X]\), the ideal \(c(f)\) generated by the coefficients of \(f\) is a regular ideal of \(A\). Let \(S\) be a non-zero submonoid of a torsion-free abelian group, \(A[S]\) the monoid ring of \(S\) over \(A\) and consider the fraction ring \(A[S]_U\) where \(U\) is the set of all regular elements \(f\) of \(A[S]\) with \((c(f))_v=A\), \(v\) being the \(v\)-operation on \(A\). In the paper cited above, the author obtained results relating certain properties of \(A\) and \(A[U]_S\). For instance, he proved that \(A\) is a Prüfer \(v\)-multiplication ring iff \(A[S]_U\) is a Prüfer ring iff \(A[S]_U\) is an \(r\)-Bezout ring, provided \(A\) is a \(v\)-ring. NEWLINENEWLINENEWLINEIn the paper under review, the author combines parts of his earlier work to extend these results to the case of an arbitrary star-operation.