Geodesic
Pseudofinite $S$-acts
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 21 (2024) no. 1, pp. 271-276 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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},
     year = {2024},
     volume = {21},
     number = {1},
     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
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
%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/

[1] J. Ax, “The elementary theory of finite fields”, Ann. Math., 88:2 (1968), 239–271 | DOI | MR | Zbl

[2] J.-L. Duret, “Les corps pseudo-finis ont la propriété d'independance”, C.R. Acad. Sei. Paris Sér. A, 290 (1980), 981–983 | MR | Zbl

[3] Z. Chatzidakis, Notes on the model theory of finite and pseudo-finite fields, CNRS-Université Paris 7, 2009 https://www.math.ens.psl.eu/z̃chatzid/papiers/Helsinki.pdf

[4] D. Macpherson, “Model theory of finite and pseudofinite groups”, Arch. Math. Logic, 57:1-2 (2018), 159–184 | DOI | MR | Zbl

[5] I.I. Pavlyuk, S.V. Sudoplatov, “Approximations for theories of abelian groups”, Mathematics and Statistics, 8:2 (2020), 220–224 | DOI | MR

[6] R. Bello-Aguirre, Model theory of finite and pseudofinite rings, PhD thesis, University of Leeds, 2016 https://etheses.whiterose.ac.uk/15771/1/RIBelloAguirrePhDThesisAug2016CORRECTED.pdf

[7] N.D. Markhabatov, “Approximations of acyclic graphs”, Izv. Irkutsk. Gos. Univ., Ser. Mat., 40 (2022), 104–111 | DOI | MR | Zbl

[8] E.L. Efremov, A.A. Stepanova, S.G. Chekanov, “Pseudofinite unars”, Algebra Logic (to appear) | MR

[9] M. Kilp, U. Knauer, A.V. Mikhalev, Monoids, acts and categories. With applications to wreath products and graphs, A handbook for students and researchers, Walter de Gruyter, Berlin, 2000 | DOI | MR | Zbl

[10] I.B. Kozhukhov, A.V. Mikhalev, “Acts over semigroups”, J. Math. Sci., New York, 269:3 (2023), 362–401 | DOI | MR | Zbl

[11] C.C. Chang, H.J. Keisler, Model theory, North-Holland Pub. Co., Amsterdam; American Elsevier, New York, 1973 | MR | Zbl

[12] E.L. Efremov, A.A. Stepanova, S.G. Chekanov, “On pseudofinite acts over finite monoids”, Algebra and Model theory, 14, eds. A.G. Pinus, E.N. Poroshenko, S.V. Sudoplatov, NSTU, Novosibirsk, 2023, 138–142 http://erlagol.ru/wp-content/uploads/cbor/erlagol_2023.pdf