Catenarian FCP ring extensions
Commutative Algebra
2019-11-26 v1
Abstract
If is a ring extension of commutative unital rings, the poset of -subalgebras of 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.
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}
}