Infinite Atomized Semilattices

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations con...

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Bibliographic Details
Main Authors:	Martin-Maroto, Fernando, Ricciardo, Antonio, Mendez, David, de Polavieja, Gonzalo G
Format:	Journal Article
Language:	English
Published:	02-11-2023
Subjects:	Mathematics - Commutative Algebra Mathematics - Rings and Algebras
Online Access:	Get full text
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Description
Summary:	We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and show that for finitely generated semilattices, atomizations consisting exclusively of non-redundant atoms always exist.
DOI:	10.48550/arxiv.2311.01389