Geodesic
Pseudofinite $S$-acts
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 271-276.

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The work has begun to study the structure of pseudofinite acts over a monoid. A theorem on the finiteness of an arbitrary cyclic subacts of $S$-act is proved under the condition that this $S$-act is pseudofinite and the number of types of isomorphisms of finite cyclic $S$-acts is finite. It is shown that a coproduct of finite $S$-acts is pseudofinite. As a consequence, it is shown that any $S$-act, where $S$ is a finite group, is pseudofinite.
Keywords: pseudofinite theory, act over monoid.
Mots-clés : pseudofinite act, coproduct 
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A. A. Stepanova; E. L. Efremov; S. G. Chekanov. Pseudofinite $S$-acts. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 271-276. http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a8/