Congruence representations of join-homomorphisms of distributive lattices: a short proof
Congruence schemes and their applications
Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.
Congruences and homomorphisms on -algebras
The topic of the paper are -algebras, where is a complete lattice. In this research we deal with congruences and homomorphisms. An -algebra is a classical algebra which is not assumed to satisfy particular identities and it is equipped with an -valued equality instead of the ordinary one. Identities are satisfied as lattice theoretic formulas. We introduce -valued congruences, corresponding quotient -algebras and -homomorphisms and we investigate connections among these notions. We prove...
Congruences and ideals in lattice effect algebras as basic algebras
Effect basic algebras (which correspond to lattice ordered effect algebras) are studied. Their ideals are characterized (in the language of basic algebras) and one-to-one correspondence between ideals and congruences is shown. Conditions under which the quotients are OMLs or MV-algebras are found.
Congruences and isotone maps on partially ordered sets.
Congruences generated by filters
Congruences, ideals and annihilators in standard QBCC-algebras
We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels.
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 of pseudocomplemented algebras
Congruences on finite lattices
Congruences on ordered groupoids.
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.
Congruences on strong semilattices of regular simple semigroups.
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.
Conjunctively polynomial-like Boolean functions.
Conjunctivity in quantales