The theory of quasivarieties constitutes an independent direction in algebra and
mathematical logic and specializes in a fragment of first-order logic-the so-called universal …

We clarify the relationship between the linear commutator and the ordinary commutator by
showing that in any variety satisfying a nontrivial idempotent Mal'cev condition the linear …

A translation in an algebraic signature is a finite conjunction of equations in one variable. On
a quasivariety K, a translation τ naturally induces a deductive system, called the τ …

In many of the familiar classes of algebras, congruences can be adequately represented by
suitable subsets of the universes of the algebras. This is a desirable phenomenon that …

Quasivarietal analogues of uniform congruence schemes are discussed, and their
relationship with the equational definability of principal relative congruences (EDPRC) is …

We present the basic theory of commutators of congruences in congruence modular
varieties (or equationally defined classes) of algebras. The theory we present was first …

We develop Commutator Theory for congruences of general algebraic systems (henceforth
called algebras) assuming only the existence of a ternary term $ d $ such that $ d (a, b …

We prove that Mal'tsev and Goursat categories may be characterized through variations of
the Shifting Lemma, that is classically expressed in terms of three congruences R, S and T …

A commutative pomonoid is a structure A=〈 A;⊕, 0;≤〉, whose reduct〈 A;⊕, 0〉 is a
commutative monoid where≤ is a partial order of A for which⊕ is isotone in both of its …

We link the recent theory of $ L $-algebras to previous notions of Universal Algebra and
Categorical Algebra concerning subtractive varieties, commutators, multiplicative lattices …