Factorable congruences and factorable congruence blocks on powers of a finite algebra
Factorable congruences and strict refinement.
Factorization and non-algebraic categories
Finite atomistic lattices that can be represented as lattices of quasivarieties
We prove that a finite atomistic lattice can be represented as a lattice of quasivarieties if and only if it is isomorphic to the lattice of all subsemilattices of a finite semilattice. This settles a conjecture that appeared in the context of [11].
Finite basis problem for 2-testable monoids
A monoid S 1 obtained by adjoining a unit element to a 2-testable semigroup S is said to be 2-testable. It is shown that a 2-testable monoid S 1 is either inherently non-finitely based or hereditarily finitely based, depending on whether or not the variety generated by the semigroup S contains the Brandt semigroup of order five. Consequently, it is decidable in quadratic time if a finite 2-testable monoid is finitely based.
Finite basis theorem for systems of semigroup identities.
Finitely axiomatizable varieties of BCK-algebras.
Finitely generated almost universal varieties of -lattices
A concrete category is (algebraically) universal if any category of algebras has a full embedding into , and is almost universal if there is a class of -objects such that all non-constant homomorphisms between them form a universal category. The main result of this paper fully characterizes the finitely generated varieties of -lattices which are almost universal.
Finitely generated relations and their applications to permutable and -permutable varieties
Finiteness conditions on EDZ-varieties
Flat semilattices
Flatness in varieties of normal bands.
Foncteur pleinement fidèle dense classant les algèbres
Frame tolerances are directly decomposable
Frattini theory for classes of finite universal algebras of Mal'tsev varieties.
Free Abelian extensions in the congruence-permutable varieties
We obtain the construction of free abelian extensions in a congurence-permutable variety V using the construction of a free abelian extension in a variety of algebras with one ternary Mal'cevoperation and a monoid of unary operations. We also use this construction to obtain a free solvable V-algebra.
Free algebras and automata realizations in the language of categories
Free algebras in varieties
We define varieties of algebras for an arbitrary endofunctor on a cocomplete category using pairs of natural transformations. This approach is proved to be equivalent to one of equational classes defined by equation arrows. Free algebras in the varieties are investigated and their existence is proved under the assumptions of accessibility.
Free algebras on a fixed set
Free almost-p-lattices