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Some applications of higher commutators in Mal’cev algebras
We establish several properties of Bulatov’s higher commutator operations in congruence permutable varieties. We use higher commutators to prove that for a finite nilpotent algebra of finite typeExpand
On subdirect decomposition and varieties of some rings with involution. II.
We give a complete description of subdirectly irreducible rings with involution satisfying x = x for some positive integer n. We also discuss ways to apply this result for constructing lattices ofExpand
Notes on Endomorphisms of Henson Graphs and their Complements
Complexity of term representations of finitary functions
The clone of term operations of an algebraic structure consists of all operations that can be expressed by a term in the language of the structure. Expand
Sequences of Commutator Operations
We look for those sequences of operations on ${{\mathbb{L}}}$ that are sequences of higher commutator operations of expansions of a finite algebra A with a Mal’cev term. Expand
Finite generation of congruence preserving functions
We investigate when the clone of congruence preserving functions is finitely generated. We obtain a full description for all finite p-groups, and for all finite algebras with Mal’cev term and simpleExpand
On Polynomials in Mal’cev Algebras
Types of polynomial completeness of expanded groups
Abstract.The polynomial functions of an algebra preserve all congruence relations. In addition, if the algebra is finite, they preserve the labelling of the congruence lattice in the sense of TameExpand
Polynomial clones of Mal’cev algebras with small congruence lattices
We show that the polynomials of every finite Mal’cev algebra with congruence lattice of height at most 2 can be described by a finite set of relations.
A b s t r a c t. Given the congruence lattice L of a finite algebra A that generates a congruence permutable variety, we look for those sequences of operations on L that have the properties of higherExpand