Factor Congruences in Semilattices
Pedro S\'anchez Terraf
TL;DR
This paper characterizes factor congruences in semilattices using generalized ideals and explores their properties when the semilattice has extremal elements, providing a deeper understanding of their algebraic structure.
Contribution
It introduces a novel characterization of factor congruences in semilattices through generalized ideals and extends classical notions to cases with extremal elements.
Findings
Factor congruences characterized via generalized ideals
Generalized ideals reduce to ordinary or dual ideals with extremal elements
Provides new insights into the structure of semilattices
Abstract
We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · Multi-Criteria Decision Making