Some characterizations of the tensor product of complete lattices with applications to quantales
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Date
2018-09-17Author
Gutiérrez García, Francisco Javier
Höhle, Ulrich
Kubiak, Tomasz
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Semigroup Forum 99 : 303-316 (2019)
Abstract
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.