On the arithmetic of monoids of ideals

Alfred Geroldinger; M. Azeem Khadam

On the arithmetic of monoids of ideals

Commutative Algebra 2021-12-07 v2

Authors: Alfred Geroldinger , M. Azeem Khadam

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 arithmetical phenomena with Krull monoids having infinite class group and prime divisors in all classes.

Keywords

monoids of ideals krull domains weakly krull mori domains r-invertible r-ideals transfer krull arithmetic structure polynomial rings

Cite

@article{arxiv.2106.00968,
  title  = {On the arithmetic of monoids of ideals},
  author = {Alfred Geroldinger and M. Azeem Khadam},
  journal= {arXiv preprint arXiv:2106.00968},
  year   = {2021}
}

Comments

Prop. 5.13 replaced Example 5.13; accepted for publication in Arkiv for Matematik

On the arithmetic of monoids of ideals

Abstract

Keywords

Cite

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