The derived sequence of a pre-Jaffard family
Commutative Algebra
2021-02-26 v1
Abstract
We introduce the concept of \emph{pre-Jaffard family}, a generalization of Jaffard families obtained by substituting the locally finite hypothesis with a much weaker compactness hypothesis. From any such family, we construct a sequence of overrings of the starting domain that allows to decompose stable semistar operations and singular length functions in more cases than what is allowed by Jaffard families. We also apply the concept to one-dimensional domains, unifying the treatment of sharp and dull degree of a Pr\"ufer domain.
Keywords
Cite
@article{arxiv.2102.12742,
title = {The derived sequence of a pre-Jaffard family},
author = {Dario Spirito},
journal= {arXiv preprint arXiv:2102.12742},
year = {2021}
}