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ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS

Part of: Semigroups General commutative ring theory Arithmetic rings and other special rings

Published online by Cambridge University Press:  08 April 2019

QINGHAI ZHONG Open the ORCID record for QINGHAI ZHONG [Opens in a new window]
QINGHAI ZHONG*
Affiliation:
University of Graz, NAWI Graz, Institute for Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria e-mail: [email protected]; https://imsc.uni-graz.at/zhong/
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Abstract

Let R be a Mori domain with complete integral closure $\widehat R$, nonzero conductor $\mathfrak f = (R: \widehat R)$, and suppose that both v-class groups ${{\cal C}_v}(R)$ and ${{\cal C}_v}(3\widehat R)$ are finite. If $R \mathfrak f$ is finite, then the elasticity of R is either rational or infinite. If $R \mathfrak f$ is artinian, then unions of sets of lengths of R are almost arithmetical progressions with the same difference and global bound. We derive our results in the setting of v-noetherian monoids.

MSC classification

Primary: 13A05: Divisibility; factorizations
Secondary: 13F05: Dedekind, Prüfer, Krull and Mori rings and their generalizations 20M13: Arithmetic theory of monoids
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 62 , Issue 2 , May 2020 , pp. 313 - 322
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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