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arXiv · 2207.04233

Multiplicative lattices: maximal implies prime and related questions

Alberto Facchini·Carmelo Antonio Finocchiaro
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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.

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Alberto Facchini, Carmelo Antonio Finocchiaro. 2022-07-09. Multiplicative lattices: maximal implies prime and related questions. https://arxiv.org/abs/2207.04233

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