We develop the theories of the strong commutator, the rectangular commutator, the strong
rectangular commutator, as well as a solvability theory for the nonmodular TC commutator …

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 …

These are notes from a multi-year learning seminar on the algebraic approach to Constraint
Satisfaction Problems (CSPs). The main topics covered are the theory of algebraic structures …

For arbitrary varieties of universal algebras, we develop the theory around the first and
second-cohomology groups characterizing extensions realizing affine datum. Restricted to …

The study of extensions realizing affine datum is specialized to central extensions in
varieties with a difference term which leads to generalizations of several classical theorems …

In a congruence modular subtractive variety there are both the commutator of ideals and the
commutator of congruences. We prove that, if I δ is the smallest congruence having an ideal …

We prove that if $\mathcal V $ is a variety of algebras (ie, an equationally axiomatizable
class of algebraic structures) in a finite language, $\mathcal V $ has a difference term, and …

The purpose of this book is to present in a uniform way commutator theory for universal
algebra. We are interested in the logical perspective of the research—emphasis is put on an …

SMB Algebras I: On the variety of SMB algebras Page 1 Filomat 37:13 (2023), 4083–4101
https://doi.org/10.2298/FIL2313083P Published by Faculty of Sciences and Mathematics …

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-
called categorical difference terms, similar to the one known in the case of varieties involving …