General mixed lattices
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910402811527168 |
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| author | Jokela, Jani |
| author_facet | Jokela, Jani |
| contents | A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and semigroups, while the more general notion of a mixed lattice remains unexplored. In this paper, we study the fundamental properties of mixed lattices and the relationships between the various properties, such as the one-sided associative, distributive and modular laws. We also give an alternative definition of mixed lattices and mixed lattice groups as non-commutative and non-associative algebras satisfying a certain set of postulates. The algebraic and the order-theoretic definitions are then shown to be equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_09064 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | General mixed lattices Jokela, Jani Combinatorics 06B75 (Primary), 06F20 (Secondary) A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and semigroups, while the more general notion of a mixed lattice remains unexplored. In this paper, we study the fundamental properties of mixed lattices and the relationships between the various properties, such as the one-sided associative, distributive and modular laws. We also give an alternative definition of mixed lattices and mixed lattice groups as non-commutative and non-associative algebras satisfying a certain set of postulates. The algebraic and the order-theoretic definitions are then shown to be equivalent. |
| title | General mixed lattices |
| topic | Combinatorics 06B75 (Primary), 06F20 (Secondary) |
| url | https://arxiv.org/abs/2205.09064 |