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 pairs for algebras abstracting Kleene and Stone algebras
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 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.
Congruences and ideals on left divisible involutory groupoids
In [1] ideals and congruences on semiloops were investigated. The aim of this paper is to generalize results obtained for semiloops to the case of left divisible involutory groupoids.
Congruences on products in varieties satisfying the CEP
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.
Connected Algebras and Universal Covering
Constructions over tournaments
We investigate tournaments that are projective in the variety that they generate, and free algebras over partial tournaments in that variety. We prove that the variety determined by three-variable equations of tournaments is not locally finite. We also construct infinitely many finite, pairwise incomparable simple tournaments.
Convex sets in algebras
Coproducts of ideal monads
The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc. 22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell. 2309 (2002) 18–32],...
Coproducts of Ideal Monads
The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by Kelly [Bull. Austral. Math. Soc.22 (1980) 1–83], its generality is reflected in its complexity which limits the applicability of this construction. Following our own research [C. Lüth and N. Ghani, Lect. Notes Artif. Intell.2309 (2002)...
Corrigendum à l'article "Sur la construction de certaines MS-algèbres" (Port. Math., 39(1-4) (1980), 489-496)
Corrigendum to "Operators and products in the lattice of existence varieties of regular semigroups".
Corrigendum to "The join of the pseudovarieties of idempotent semigroups and locally trivial semigroups".
Covering condition in the lattice of radical classes of linearly ordered groups
Covers in the lattice of varieties of -groups.