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ON THE ARITHMETIC OF MORI MONOIDS AND DOMAINS

Published online by Cambridge University Press:  08 April 2019

QINGHAI ZHONG
Affiliation:
University of Graz, NAWI Graz, Institute for Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria e-mail: qinghai.zhong@uni-graz.at; https://imsc.uni-graz.at/zhong/
Corresponding
E-mail address:

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2019

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