SpringerLink
Log in

Congruence-Permutable \( S \)-Acts

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

An algebra is congruence-permutable if its congruences commute under composition. Many familiar varieties of algebras, such as the variety of groups, consist of congruence-permutable algebras, but the variety of \( S \)-acts have not congruence-permutable members. We describe congruence-permutable \( S \)-acts in the cases that \( S \) is a commutative monoid or a group.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Khaliullina A. R., “Congruences of the acts over groups,” in: Proceedings of the 20th All-Russia Interuniversity Scientific-Technological Conference of Students and Postgraduates “Microelectronics and Informatics–2013”, MIET, Moscow (2013), 148.

  2. Stepanova A. A., “\( S \)-Acts over a well-ordered monoid with modular congruence lattice,” The Bulletin of Irkutsk State University. Ser. Math., vol. 35, 87–102 (2021).

    Article  MathSciNet  Google Scholar 

  3. Stepanova A. A. and Trikashnaya N. V., “The strongly faithful \( S \)-acts over commutative monoids and groups with modular congruence lattices,” Sib. Electr. Math. Reports, vol. 13, 1067–1077 (2016).

    MathSciNet  MATH  Google Scholar 

  4. Kilp M., Knauer U., and Mikhalev A. V., Monoids, Acts and Categories: with Applications to Wreath Products and Graphs. A Handbook for Students and Researchers, De Gruyter, Berlin and New York (2000).

    Book  Google Scholar 

  5. Malcev A. I., Algebraic Systems, Springer and Akademie, Berlin, Heidelberg, and New York (1973).

    Book  Google Scholar 

  6. Stepanova A. A. and Ptakhov D. O., “Axiomatizability of the class of subdirectly irreducible acts over an abelian group,” Algebra Logic, vol. 59, no. 5, 395–403 (2020).

    Article  MathSciNet  Google Scholar 

Download references

Funding

The work was supported by the Ministry of Science and Education of the Russian Federation (Agreement 075–02–2021–1395 of 01.06.2021).

Author information

Authors and Affiliations

  1. Far Eastern Federal University, Vladivostok, Russia

    A. A. Stepanova & S. G. Chekanov

Authors
  1. A. A. Stepanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. G. Chekanov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Stepanova.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 202–208. https://doi.org/10.33048/smzh.2022.63.114

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanova, A.A., Chekanov, S.G. Congruence-Permutable \( S \)-Acts. Sib Math J 63, 167–172 (2022). https://doi.org/10.1134/S0037446622010141

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446622010141

Keywords

UDC

Search

Navigation