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