Some structural and residual properties of 2-semilattices
| Autor: | Ian Payne |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Property (philosophy) 010102 general mathematics Digraph 0102 computer and information sciences Congruence relation Type (model theory) Residual 01 natural sciences 010201 computation theory & mathematics Simple (abstract algebra) Order (group theory) 0101 mathematics Variety (universal algebra) Mathematics |
| Zdroj: | Algebra universalis. 81 |
| ISSN: | 1420-8911 0002-5240 |
| Popis: | To each 2-semilattice, one can associate a digraph and a partial order. We analyze these two structures working toward two main goals: One goal is to give a structural dichotomy on minimal congruences of 2-semilattices. From this, we are able to deduce information about the tame-congruence-theoretic types that occur in 2-semilattices. In particular, we show that the type of a finite simple 2-semilattice is always either 3 or 5 and can be deduced immediately from its associated digraph. The other goal is to introduce and explore a property that some 2-semilattices have which we have named the “component-semilattice property”. We show that this property must hold in every algebra in a variety of 2-semilattices that is both locally finite and residually small. Hence, a finite 2-semilattice that lacks this property generates a residually large variety. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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