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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{SEMR_2024_21_1_a8,
     author = {A. A. Stepanova and E. L. Efremov and S. G. Chekanov},
     title = {Pseudofinite $S$-acts},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {271--276},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {2024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a8/}
}
TY  - JOUR
AU  - A. A. Stepanova
AU  - E. L. Efremov
AU  - S. G. Chekanov
TI  - Pseudofinite $S$-acts
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2024
SP  - 271
EP  - 276
VL  - 21
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a8/
LA  - en
ID  - SEMR_2024_21_1_a8
ER  - 
%0 Journal Article
%A A. A. Stepanova
%A E. L. Efremov
%A S. G. Chekanov
%T Pseudofinite $S$-acts
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2024
%P 271-276
%V 21
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2024_21_1_a8/
%G en
%F SEMR_2024_21_1_a8
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/