Multiplicative lattices: maximal implies prime and related questions
Rings and Algebras
2022-07-12 v1
Abstract
The goal of this paper is to deepen the study of multiplicative lattices in the sense of Facchini, Finocchiaro and Janelidze. We provide a sort of Prime Ideal Principle that guarantees that maximal implies prime in a variety of cases (among them the case of commutative rings with identity). This result is used to study the lattice theoretic counterpart of multiplicative closed sets, that of m-systems. The notion of m-system is also studied from the topological point of view.
Keywords
Cite
@article{arxiv.2207.04233,
title = {Multiplicative lattices: maximal implies prime and related questions},
author = {Alberto Facchini and Carmelo Antonio Finocchiaro},
journal= {arXiv preprint arXiv:2207.04233},
year = {2022}
}