Decomposition and classification of length functions
Commutative Algebra
2018-07-18 v1 Rings and Algebras
Abstract
We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain admits a Jaffard family, when it is Noetherian and when it is a Pr\"ufer domains such that every ideal has only finitely many minimal primes. We also show that there is a natural bijective correspondence between singular length functions and localizing systems.
Cite
@article{arxiv.1807.06396,
title = {Decomposition and classification of length functions},
author = {Dario Spirito},
journal= {arXiv preprint arXiv:1807.06396},
year = {2018}
}