Cancellative actions
The following problem is considered: when can the action of a cancellative semigroup on a set be extended to a simply transitive action of the universal group of on a larger set.
Characters and the structure of finite semigroups.
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 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.
Completely 0-simple semigroups and their associated graphs and groups.
Completely regular semigroups as semigroups of partial transformations.
Congruence-preserving endomorphisms.
Conjugation in semigroups and finite dimensional algebras
Construction and representation of regular semigroups.
Construction of medial semigroups
Countable Hausdorff spaces with countable weight