Vol. 318, No. 2, 2022

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Semigroup rings as weakly Krull domains

Gyu Whan Chang, Victor Fadinger and Daniel Windisch

Vol. 318 (2022), No. 2, 433–452
Abstract

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

Keywords
semigroup ring, weakly Krull domain, finite $t$-character, system of sets of lengths
Mathematical Subject Classification
Primary: 13A15, 13F05, 20M12
Milestones
Received: 24 January 2022
Revised: 21 April 2022
Accepted: 21 May 2022
Published: 20 August 2022
Authors
Gyu Whan Chang
Department of Mathematics Education
Incheon National University
Incheon
South Korea
Victor Fadinger
Institute for Mathematics and Scientific Computing
NAWI Graz
University of Graz
Graz
Austria
Daniel Windisch
Institute for Analysis and Number Theory
NAWI Graz
Graz University of Technology
Graz
Austria