On seminormal semigroups
This paper studies the semigroup analogs of results about seminormal overrings from [Commun. Algebra 10, 1421-1448 (1982; Zbl 0496.13001)]\ by \textit{D. Dobbs, J. Huckaba}, and the reviewer. A (nonzero) commutative, torsion-free cancellative semigroup \(S\) with 0, written additively and with quotient \(G\), is said to be seminormal if whenever \(2a,3a\in S\) for \(a\in G\), then \(a\in S\). Two of the main results for one-dimensional semigroups are (1) if \(S\) is seminormal, then each integral oversemigroup of \(S\) is seminormal, and (2) each oversemigroup of \(S\) is seminormal if and only if both \(S\) is seminormal and its integral closure \(S'\) is a valuation semigroup.
commutative torsion-free cancellative semigroups
scientific article; zbMATH DE number 1145424