Directly decomposable congruences in varieties with nullary operations
Distributed families of varieties of algebras
Distributive multisemilattices [Book]
Equational bases for weak monounary varieties
It is well-known that every monounary variety of total algebras has one-element equational basis (see [5]). In my paper I prove that every monounary weak variety has at most 3-element equational basis. I give an example of monounary weak variety having 3-element equational basis, which has no 2-element equational basis.
Equational theories of some almost unary groupoids
Even equations and Agassiz sums
Every at most four element algebra has a Mal'cev theory for permutability
Factorable congruences and factorable congruence blocks on powers of a finite algebra
Finite basis theorem for systems of semigroup identities.
Finitely axiomatizable varieties of BCK-algebras.
Finitely generated relations and their applications to permutable and -permutable varieties
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 systems of algebras and ultraclosed classes.
Galois theory and double central extensions.
Generalization of the concept of variety and quasivariety to partial algebras through category theory [Book]
Generalized deductive systems in subregular varieties
An algebra is subregular alias regular with respect to a unary term function if for each we have whenever for each . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset is a class of some congruence on containing if and only if is this generalized deductive system. This method is efficient (needs a finite number of steps).
Hereditary properties of algebras with respect to inductive limits
Hyperassociative varieties of semigroups.
Hyperidentities and hypervarieties.