Semigroup rings as weakly Krull domains

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 $(0, 0, 0, \dots)$ (resp., type $(0, 0, 0, \dots)$ except $p$ ). Moreover, we give arithmetical applications of this result.

PDF Access Denied

We have not been able to recognize your IP address 3.145.151.141 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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

Vol. 318, No. 2, 2022

Gyu Whan Chang, Victor Fadinger and Daniel Windisch

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors