Finitely generated congruence distributive quasivarieties of algebras
Finitely generated relations and their applications to permutable and -permutable varieties
Finitely generated universal varieties of distributive double -algebras
Finiteness conditions on EDZ-varieties
Finite-to-finite universal varieties of distributive double -algebras
Flat semilattices
Flatness in varieties of normal bands.
Flocks in universal and Boolean algebras
We propose the notion of flocks, which formerly were introduced only in based algebras, for any universal algebra. This generalization keeps the main properties we know from vector spaces, e.g. a closure system that extends the subalgebra one. It comes from the idempotent elementary functions, we call "interpolators", that in case of vector spaces merely are linear functions with normalized coefficients. The main example, we consider outside vector spaces, concerns Boolean algebras,...
Foldness of Commutative Ideals in BCK-algebras
This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.
Foncteur pleinement fidèle dense classant les algèbres
Formal integration in composition rings
Formal Translation Monoid and Algebra Congruences in a Monodial Category.
Formulas and ultraproducts in categories
Four notes on quasiorder lattices
Four-part semigroups - semigroups of Boolean operations
Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g,...,g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green's relations, and prove a representation theorem for four-part semigroups.
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.