English

Flat Ideals and Stability in Integral Domains

Commutative Algebra 2010-01-29 v1

Abstract

We introduce the concept of \textit{quasi-stable} ideal in an integral domain DD (a nonzero fractional ideal II of DD is quasi-stable if it is flat in its endomorphism ring (I ⁣:I)(I \colon I)) and study properties of domains in which each nonzero fractional ideal is quasi-stable. We investigate some questions about flatness that were raised by S. Glaz and W.V. Vasconcelos in their 1977 paper \cite{GV}.

Keywords

Cite

@article{arxiv.1001.5224,
  title  = {Flat Ideals and Stability in Integral Domains},
  author = {Giampaolo Picozza and Francesca Tartarone},
  journal= {arXiv preprint arXiv:1001.5224},
  year   = {2010}
}

Comments

16 pages

R2 v1 2026-06-21T14:40:49.184Z