A constructive “Closed subgroup theorem” for localic groups and groupoids
A decomposition of homomorphic images of nearlattices
By a nearlattice is meant a join-semilattice where every principal filter is a lattice with respect to the induced order. The aim of our paper is to show for which nearlattice and its element the mapping is a (surjective, injective) homomorphism of into .
A note on cylindric lattices
0. Introduction. Besides being of intrinsic interest, cylindric (semi-) lattices arise naturally from the study of dependencies in relational databases; the polynomials on a cylindric semilattice are closely related to the queries obtainable from project-join mappings on a relational database (cf. [D] for references). This note is intended to initiate the study of these structures, and only a few, rather basic results will be given. Some problems at the end will hopefully stimulate further research....
A note on the prime ideal theorem
A scheme for congruence semidistributivity
A diagrammatic statement is developed for the generalized semidistributive law in case of single algebras assuming that their congruences are permutable. Without permutable congruences, a diagrammatic statement is developed for the ∧-semidistributive law.
A ternary variety generated by lattices
bi-BL-algebra
In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.
Boolean graphs
Calcul des idéaux d'un ordonné fini
Canonical partition theorems for finite distributive lattices
Cocycle condition for multi-pullbacks of algebras
Take finitely many topological spaces and for each pair of these spaces choose a pair of corresponding closed subspaces that are identified by a homeomorphism. We note that this gluing procedure does not guarantee that the building pieces, or the gluings of some pieces, are embedded in the space obtained by putting together all given ingredients. Dually, we show that a certain sufficient condition, called the cocycle condition, is also necessary to guarantee sheaf-like properties of surjective multi-pullbacks...
Conception de plans d'expériences ou d'enquêtes permutables distributifs
Congruence extension from a semilattice to the freely generated distributive lattice
Cyclic ordered groups and MV-algebras
Diameters in locales: How bad they can be
Die primitiven Klassen arithmetischer Ringe.
Embedding of semilattices into distributive lattices
Errata to the paper “On paracompact locales and metric locales”
Fan-Gottesman type compactification of frames
Finite closed coverings of compact quantum spaces
We consider the poset of all non-empty finite subsets of the set of natural numbers, use the poset structure to topologise it with the Alexandrov topology, and call the thus obtained topological space the universal partition space. Then we show that it is a classifying space for finite closed coverings of compact quantum spaces in the sense that any such a covering is functorially equivalent to a sheaf over this partition space. In technical terms, we prove that the category of finitely supported...