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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.

Cayley color graphs of inverse semigroups and groupoids

Nándor Sieben (2008)

Czechoslovak Mathematical Journal

The notion of Cayley color graphs of groups is generalized to inverse semigroups and groupoids. The set of partial automorphisms of the Cayley color graph of an inverse semigroup or a groupoid is isomorphic to the original inverse semigroup or groupoid. The groupoid of color permuting partial automorphisms of the Cayley color graph of a transitive groupoid is isomorphic to the original groupoid.

Certain partial orders on semigroups

Mario Petrich (2001)

Czechoslovak Mathematical Journal

Relations introduced by Conrad, Drazin, Hartwig, Mitsch and Nambooripad are discussed on general, regular, completely semisimple and completely regular semigroups. Special properties of these relations as well as possible coincidence of some of them are investigated in some detail. The properties considered are mainly those of being a partial order or compatibility with multiplication. Coincidences of some of these relations are studied mainly on regular and completely regular semigroups.

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