Arkiv för Matematik
Volume 60 (2022)
On the arithmetic of monoids of ideals
Pages: 67 – 106
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.
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