Algebras describing pseudocomplemented, relatively pseudocomplemented and sectionally pseudocomplemented posets
| Autor: | Ivan Chajda, Helmut Länger |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
congruence permutability Physics and Astronomy (miscellaneous) General Mathematics 0102 computer and information sciences 01 natural sciences relatively pseudocomplemented poset congruence distributivity Congruence (geometry) 06A11 06D15 08A62 08B05 commutative directoid Computer Science (miscellaneous) FOS: Mathematics QA1-939 Order (group theory) Universal algebra weak regularity Mathematics - Combinatorics 0101 mathematics Algebra over a field Commutative property Mathematics Stone poset Mathematics::Combinatorics 010102 general mathematics λ-lattice Mathematics - Rings and Algebras 010201 computation theory & mathematics Chemistry (miscellaneous) Rings and Algebras (math.RA) pseudocomplemented poset Computer Science::Programming Languages Combinatorics (math.CO) sectionally pseudocomplemented poset Symmetry (geometry) Partially ordered set MathematicsofComputing_DISCRETEMATHEMATICS |
| Zdroj: | Symmetry, Vol 13, Iss 753, p 753 (2021) Symmetry Volume 13 Issue 5 |
| Popis: | In order to be able to use methods of universal algebra for investigating posets, we assigned to every pseudocomplemented poset, to every relatively pseudocomplemented poset and to every sectionally pseudocomplemented poset, a certain algebra (based on a commutative directoid or on a λ-lattice) which satisfies certain identities and implications. We show that the assigned algebras fully characterize the given corresponding posets. A certain kind of symmetry can be seen in the relationship between the classes of mentioned posets and the classes of directoids and λ-lattices representing these relational structures. As we show in the paper, this relationship is fully symmetric. Our results show that the assigned algebras satisfy strong congruence properties which can be transferred back to the posets. We also mention applications of such posets in certain non-classical logics. |
| Databáze: | OpenAIRE |
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