Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties
Regularity in arithmetical varieties
Relative congruence distributivity within quasivarieties of nearly associative Φ-algebras
Relatively pseudocomplemented directoids
The concept of relative pseudocomplement is introduced in a commutative directoid. It is shown that the operation of relative pseudocomplementation can be characterized by identities and hence the class of these algebras forms a variety. This variety is congruence weakly regular and congruence distributive. A description of congruences via their kernels is presented and the kernels are characterized as the so-called -ideals.
Semiregularity of congruences implies congruence modularity at 0
We introduce a weakened form of regularity, the so called semiregularity, and we show that if every diagonal subalgebra of is semiregular then is congruence modular at 0.
Strictly order primal algebras.
Subalgebras and homomorphic images of algebras having the CEP and the WCIP
In the present paper we consider algebras satisfying both the congruence extension property (briefly the CEP) and the weak congruence intersection property (WCIP for short). We prove that subalgebras of such algebras have these properties. We deduce that a lattice has the CEP and the WCIP if and only if it is a two-element chain. We also show that the class of all congruence modular algebras with the WCIP is closed under the formation of homomorphic images.
Subdirectly irreducible and congruence distributive -lattices
The congruence lattice of implication algebras.
The congruence variety of metabelian groups is not self-dual.
The egg-box property of congruences
The structure of the rings assigned to group varieties
The weak extension property and finite axiomatizability for quasivarieties
We define and compare a selection of congruence properties of quasivarieties, including the relative congruence meet semi-distributivity, RSD(∧), and the weak extension property, WEP. We prove that if 𝒦 ⊆ ℒ ⊆ ℒ' are quasivarieties of finite signature, and ℒ' is finitely generated while 𝒦 ⊨ WEP, then 𝒦 is finitely axiomatizable relative to ℒ. We prove for any quasivariety 𝒦 that 𝒦 ⊨ RSD(∧) iff 𝒦 has pseudo-complemented congruence lattices and 𝒦 ⊨ WEP. Applying these results and other results...
Tolerance distributive and tolerance Boolean varieties of semigroups
Tolerance distributive and tolerance modular varieties of commutative semigroups
Tolerance modular varieties of semigroups
Tolerances and congruences on implication algebras
Tolerances in congruence permutable algebras
Trapezoid lemma and congruence distributivity
Varieties having directly decomposable congruence classes