Infinite Atomized Semilattices
Commutative Algebra
2025-11-25 v2 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.2311.01389,
title = {Infinite Atomized Semilattices},
author = {Fernando Martin-Maroto and Antonio Ricciardo and David Mendez and Gonzalo G. de Polavieja},
journal= {arXiv preprint arXiv:2311.01389},
year = {2025}
}
Comments
25 pages, 2 figures