Radical factorization in finitary ideal systems
Commutative Algebra
2019-06-25 v2
Abstract
In this paper we investigate the concept of radical factorization with respect to finitary ideal systems of cancellative monoids. We present new characterizations for r-almost Dedekind r-SP-monoids and provide specific descriptions of t-almost Dedekind t-SP-monoids and w-SP-monoids. We show that a monoid is a w-SP-monoid if and only if the radical of every nontrivial principal ideal is t-invertible. We characterize when the monoid ring is a w-SP-domain and describe when the *-Nagata ring is an SP-domain for a star operation * of finite type.
Keywords
Cite
@article{arxiv.1903.09237,
title = {Radical factorization in finitary ideal systems},
author = {Bruce Olberding and Andreas Reinhart},
journal= {arXiv preprint arXiv:1903.09237},
year = {2019}
}