English

On the arithmetic of stable domains

Commutative Algebra 2021-05-11 v2

Abstract

A commutative ring RR is stable if every non-zero ideal II of RR is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 22-generator property. In the present paper we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.

Keywords

Cite

@article{arxiv.2007.05574,
  title  = {On the arithmetic of stable domains},
  author = {Aqsa Bashir and Alfred Geroldinger and Andreas Reinhart},
  journal= {arXiv preprint arXiv:2007.05574},
  year   = {2021}
}

Comments

This paper has been accepted for publication in the Communications in Algebra

R2 v1 2026-06-23T17:01:52.828Z