The strong amalgamation property
The strong amalgamation property and (effective) codescent morphisms.
The structure of the rings assigned to group varieties
The variety covering the variety of all modular lattices.
The variety generated by tournaments
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...
The weak hereditary class of a variety
We study the weak hereditary class of all weak subalgebras of algebras in a total variety . We establish an algebraic characterization, in the sense of Birkhoff’s HSP theorem, and a syntactical characterization of these classes. We also consider the problem of when such a weak hereditary class is weak equational.
The word problem for regular identities
Three Mal'cev Type Theorems and their Application
Three-variable equations of posets
We find an independent base for three-variable equations of posets.
Tolerance distributive and tolerance Boolean varieties of semigroups
Tolerance distributive and tolerance modular varieties of commutative semigroups
Tolerance modular varieties of semigroups
Tolerance numbers, congruence -permutability and BCK-algebras
Tolerances and congruences on implication algebras
Tolerances and the Chinese remainder theorem
Tolerances in congruence permutable algebras
Transferable principal congruences and regular algebras
Transitivity of principal tolerances is not a Mal'cev property
Trapezoid lemma and congruence distributivity