Semigroups and semigroup rings (Q2785948)

Let \(S\) be a nonzero submonoid of an additive torsion-free abelian group, \(R\) a commutative ring with 1, and \(R[S]\) the semigroup ring of \(S\) over \(R\). In this paper, the author reports on some of his recent results concerning the ideal theory of \(S\) and \(R[S]\). Some of the ring-theoretic topics (together with semigroup versions for \(S)\) discussed include star-operations, inert extensions, cancellation ideals, seminormality, PVMDs and PVDs. More detailed accounts with proofs will appear elsewhere.NEWLINENEWLINEFor the entire collection see [Zbl 0855.00015].