Arkiv för Matematik

Volume 60 (2022)

Number 1

On the arithmetic of monoids of ideals

Pages: 67 – 106

DOI: https://dx.doi.org/10.4310/ARKIV.2022.v60.n1.a4

Authors

Alfred Geroldinger (Institute of Mathematics and Scientific Computing, University of Graz, Austria)

M. Azeem Khadam (Institute of Mathematics and Scientific Computing, University of Graz, Austria)

Abstract

We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of $r$-invertible $r$-ideals for certain ideal systems $r$) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetic phenomena with Krull monoids having infinite class group and prime divisors in all classes.

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This work was supported by the Austrian Science Fund FWF, Project P33499-N.

Received 1 June 2021

Received revised 21 November 2021

Accepted 6 December 2021

Published 16 May 2022