Semi-abelian monadic categories.
Semidirectly closed pseudovarieties of locally trivial semigroups.
Solvability of equations in varieties of universal algebras.
Some pseudovariety joins involving the pseudovariety of finite groups.
Some quasi-ordered classes of finite commutative semigroups.
Some regular quasivarieties of commutative binary modes
Irregular (quasi)varieties of groupoids are (quasi)varieties that do not contain semilattices. The regularization of a (strongly) irregular variety of groupoids is the smallest variety containing and the variety of semilattices. Its quasiregularization is the smallest quasivariety containing and . In an earlier paper the authors described the lattice of quasivarieties of cancellative commutative binary modes, i.e. idempotent commutative and entropic (or medial) groupoids. They are all irregular...
Some results on the dot-depth hierarchy.
Split extensions and semidirect products of unitary magmas
We develop a theory of split extensions of unitary magmas, which includes defining such extensions and describing them via suitably defined semidirect product, yielding an equivalence between the categories of split extensions and of (suitably defined) actions of unitary magmas on unitary magmas. The class of split extensions is pullback stable but not closed under composition. We introduce two subclasses of it that have both of these properties.
Strong regular varieties of partial algebras I
Subdirect representations in axiomatic classes
Subsemigroups of completely simple semigroups. III.
Sur La Logique De Premier Ordre Et La Théorie Des Catégories.
Sur le rang et la définissabilité des opérations implicites dans les classes d'algèbres