Concrete representation of some equivalence lattices
Conditions de Mal'cev et algèbres universelles uniformes
Conditions for factorable relations
Conditions for independence of varieties
Conditions for transitive principal tolerances
Conditions for trivial principal tolerances
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 classes in regular varieties.
Congruence distributivity and modularity permit tolerances
Congruence distributivity in varieties with constants
Congruence lattices in varieties with compact intersection property
We say that a variety of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in and embeddings between them. We believe that the strategy used here can...
Congruence lattices of intransitive G-Sets and flat M-Sets
An M-Set is a unary algebra whose set of operations is a monoid of transformations of ; is a G-Set if is a group. A lattice is said to be represented by an M-Set if the congruence lattice of is isomorphic to . Given an algebraic lattice , an invariant is introduced here. provides substantial information about properties common to all representations of by intransitive G-Sets. is a sublattice of (possibly isomorphic to the trivial lattice), a -product lattice. A -product...
Congruence pairs for algebras abstracting Kleene and Stone algebras
Congruence properties of distributive double -algebras
Congruence relations on direct products of lattices
Congruence relations on finitary models
Congruence restrictions on axes
We give Mal’cev conditions for varieties 4V4 whose congruences on the product , are determined by their restrictions on the axes in .
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.
Congruence semimodularity of conservative groupoids
Congruence submodularity
We present a countable infinite chain of conditions which are essentially weaker then congruence modularity (with exception of first two). For varieties of algebras, the third of these conditions, the so called 4-submodularity, is equivalent to congruence modularity. This is not true for single algebras in general. These conditions are characterized by Maltsev type conditions.