2022/07/09 by Alberto Facchini, Facchini, Alberto, Carmelo Antonio Finocchiaro +1
Computer Science · Mathematics · #06B23 #06B99 #13A15 #16D25 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2207.04233
openalex publication_date 2022/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.