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Cancellative actions

Pierre Antoine Grillet (2003)

Commentationes Mathematicae Universitatis Carolinae

The following problem is considered: when can the action of a cancellative semigroup S on a set be extended to a simply transitive action of the universal group of S on a larger set.

Commutation of operations and its relationship with Menger and Mann superpositions

Fedir M. Sokhatsky (2004)

Discussiones Mathematicae - General Algebra and Applications

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 zeropotent semigroups with few invariant congruences

Robert El Bashir, Tomáš Kepka (2008)

Czechoslovak Mathematical Journal

Commutative semigroups satisfying the equation 2 x + y = 2 x and having only two G -invariant congruences for an automorphism group G are considered. Some classes of these semigroups are characterized and some other examples are constructed.

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