Some characterizations of the tensor product of complete lattices with applications to quantales
This paper examines tensor products of complete lattices in which one factor is com- pletely distributive. At least five characterizations of complete distributivity involving tensor products of complete lattices are given, among them this one: M is a completely distributive lattice if and only if f...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad del País Vasco |
| Repositorio: | Addi. Archivo Digital para la Docencia y la Investigación |
| OAI Identifier: | oai:addi.ehu.eus:10810/65063 |
| Acceso en línea: | http://hdl.handle.net/10810/65063 |
| Access Level: | acceso abierto |
| Palabra clave: | complete distributivity tensor product quantale |
| Sumario: | This paper examines tensor products of complete lattices in which one factor is com- pletely distributive. At least five characterizations of complete distributivity involving tensor products of complete lattices are given, among them this one: M is a completely distributive lattice if and only if for every complete lattice L the tensor product M ⊗ L is order isomorphic to the partially ordered set of all join- and meet-reversing maps from the complete lattice of all upclosed subsets of L to the lattice M. Some of these characterizations are then applied to give explicit descriptions of the multiplication of the tensor product of two quantales one of which is completely distributive. |
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