Complete co-atomic lattices with enough primes.
Completely subdirect products of directed sets
This paper deals with directly indecomposable direct factors of a directed set.
Completion of a class of topological semilattices, applications. (Complétion d'une classe de demi-treillis topologiques, applications.)
Completions for partially ordered semigroups.
Concept lattices of quasiordered sets
Conception de plans d'expériences ou d'enquêtes permutables distributifs
Congruence classes in Brouwerian semilattices
Brouwerian semilattices are meet-semilattices with 1 in which every element a has a relative pseudocomplement with respect to every element b, i. e. a greatest element c with a∧c ≤ b. Properties of classes of reflexive and compatible binary relations, especially of congruences of such algebras are described and an abstract characterization of congruence classes via ideals is obtained.
Congruence extension from a semilattice to the freely generated distributive lattice
Congruence kernels of distributive PJP-semilattices
A meet semilattice with a partial join operation satisfying certain axioms is a JP-semilattice. A PJP-semilattice is a pseudocomplemented JP-semilattice. In this paper we describe the smallest PJP-congruence containing a kernel ideal as a class. Also we describe the largest PJP-congruence containing a filter as a class. Then we give several characterizations of congruence kernels and cokernels for distributive PJP-semilattices.
Congruence lattices of finite chains with endomorphisms
Characterization of congruence lattices of finite chains with either one or two endomorphisms is given.
Congruence relations on finitary models
Congruences and isotone maps on partially ordered sets.
Congruences generated by filters
Congruences in ordered sets
A concept of congruence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
Congruences in ordered sets and LU compatible equivalences
A concept of equivalence preserving upper and lower bounds in a poset is introduced. If is a lattice, this concept coincides with the notion of lattice congruence.
Congruences on pseudocomplemented semilattices
It is known that congruence lattices of pseudocomplemented semilattices are pseudocomplemented [4]. Many interesting properties of congruences on pseudocomplemented semilattices were described by Sankappanavar in [4], [5], [6]. Except for other results he described congruence distributive pseudocomplemented semilattices [6] and he characterized pseudocomplemented semilattices whose congruence lattices are Stone, i.e. belong to the variety B₁ [5]. In this paper we give a partial solution to a more...
Congruences on semilattices with section antitone involutions
We deal with congruences on semilattices with section antitone involution which rise e.g., as implication reducts of Boolean algebras, MV-algebras or basic algebras and which are included among implication algebras, orthoimplication algebras etc. We characterize congruences by their kernels which coincide with semilattice filters satisfying certain natural conditions. We prove that these algebras are congruence distributive and 3-permutable.
Conjugated algebras
We generalize the correspondence between basic algebras and lattices with section antitone involutions to a more general case where no lattice properties are assumed. These algebras are called conjugated if this correspondence is one-to-one. We get conditions for the conjugary of such algebras and introduce the induced relation. Necessary and sufficient conditions are given to indicated when the induced relation is a quasiorder which has “nice properties", e.g. the unary operations are antitone...
Conjugately Factorable Isotone Self-Mappings Of Complete Lattices
Conjugately factorable isotone self-mappings of complete lattices.