Combinatorics of the free Baxter algebra.
Commutation of operations and its relationship with Menger and Mann superpositions
The article considers a problem from Trokhimenko paper [13] concerning the study of abstract properties of commutations of operations and their connection with the Menger and Mann superpositions. Namely, abstract characterizations of some classes of operation algebras, whose signature consists of arbitrary families of commutations of operations, Menger and Mann superpositions and their various connections are found. Some unsolved problems are given at the end of the article.
Commutative directoids with sectionally antitone bijections
We study commutative directoids with a greatest element, which can be equipped with antitone bijections in every principal filter. These can be axiomatized as algebras with two binary operations satisfying four identities. A minimal subvariety of this variety is described.
Commutative quasi-trivial superassociative systems
Commutative semigroups that are simple over thein endomorphism semirings
Commutative semigroups whose lattice of tolerances is Boolean
Commutative semigroups with almost transitive endomorphism semirings
Commutative semigroups with few fully invariant congruences I.
Commutative semigroups with few fully invariant congruences II.
Commutative zeropotent semigroups with few invariant congruences
Commutative semigroups satisfying the equation and having only two -invariant congruences for an automorphism group are considered. Some classes of these semigroups are characterized and some other examples are constructed.
Commutativity of Operators on the Lattice of Existence Varieties.
Commutator theory in strongly protomodular categories.
Compact elements in the lattice of varieties
We prove that the lattice of varieties contains almost no compact elements.
Compact elements of the lattice of congruences in an algebra
Compact universal relation in varieties with constants
Compactness and homomorphisms of algebraic structures
Compatible Idempotent Terms in Universal Algebra
In universal algebra, we oftentimes encounter varieties that are not especially well-behaved from any point of view, but are such that all their members have a “well-behaved core”, i.e. subalgebras or quotients with satisfactory properties. Of special interest is the case in which this “core” is a retract determined by an idempotent endomorphism that is uniformly term definable (through a unary term ) in every member of the given variety. Here, we try to give a unified account of this phenomenon....
Compatible relations on algebras
Compatible tolerances on groupoids
Complements of congruences in an -group