Factorization and non-algebraic categories
Finiteness conditions on EDZ-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
Free entropic groupoids
Free groupoids in varieties determined by a short equation
Free groupoids with axioms of the form and/or .
Free groupoids with . II.
Free Objects in Primitive Varieties of N-groupoids
Free -distributive lattice over an -element chain.
Free Suslin algebras
Free systems of algebras and ultraclosed classes.
Free Term Algebras
We interoduce a new characterization of algebras of normal forms of term rewriting systems [35] as algerbras of term free in itself (any function from free generators into the algebra generates endomorphism of the algebra). Introduced algebras are free in classes of algebras satisfying some sets of equalities. Their universes are subsets of all terms and the denotations of operation symbols are partially identical with the operations of construction of terms. These algebras are compiler algebras...
Functorial algebras and automata