English

Catenarian FCP ring extensions

Commutative Algebra 2019-11-26 v1

Abstract

If RSR\subseteq S is a ring extension of commutative unital rings, the poset [R,S][R,S] of RR-subalgebras of SS is called catenarian if it verifies the Jordan-H\"older property. This property has already been studied by Dobbs and Shapiro for finite extensions of fields. We investigate this property for arbitrary ring extensions, showing that many type of extensions are catenarian. We reduce the characterization of catenarian extensions to the case of field extensions, an unsolved question at that time.

Keywords

Cite

@article{arxiv.1911.10577,
  title  = {Catenarian FCP ring extensions},
  author = {Gabriel Picavet and Martine Picavet-L'Hermitte},
  journal= {arXiv preprint arXiv:1911.10577},
  year   = {2019}
}
R2 v1 2026-06-23T12:25:38.478Z