Semigroup rings as weakly Krull domains

Abstract

Let $D$ be an integral domain and $\Gamma$ be a torsion-free commutative cancellative (additive) semigroup with identity element and quotient group $G$. In this paper, we show that if char$(D)=0$ (resp., char$(D)=p>0$), then $D[\Gamma ]$ is a weakly Krull domain if and only if $D$ is a weakly Krull UMT-domain, $\Gamma$ is a weakly Krull UMT-monoid, and $G$ is of type $(0,0,0,\dots )$ (resp., type $(0,0,0,\dots )$ except $p$). Moreover, we give arithmetical applications of this result.

References in corpus (4)

• On strongly primary monoids, with a focus on Puiseux monoids
• A construction of integer-valued polynomials with prescribed sets of lengths of factorizations
• Sets of lengths of factorizations of integer-valued polynomials on Dedekind domains with finite residue fields
• Graded integral domains which are UMT-domains

Cited by in corpus (2)

• Factorization under Local Finiteness Conditions
• On transfer homomorphisms in commutative rings with zero-divisors