Descending chains of semistar operations
Commutative Algebra
2017-11-16 v1
Abstract
A class of integer-valued functions defined on the set of ideals of an integral domain is investigated. We show that this class of functions, which we call ideal valuations, are in one-to-one correspondence with countable descending chains of finite type, stable semistar operations with largest element equal to the -operation. We use this class of functions to recover familiar semistar operations such as the -operation and to give a solution to a conjecture by Chapman and Glaz when the ring is a valuation domain.
Keywords
Cite
@article{arxiv.1711.05399,
title = {Descending chains of semistar operations},
author = {Hyun Seung Choi and Timothy McEldowney and Andrew Walker},
journal= {arXiv preprint arXiv:1711.05399},
year = {2017}
}