Skip to main content
SpringerLink
Log in

\( P \)-Stability of Some Classes of \( S \)-Acts

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

The notion of \( P \)-stability is a particular case of the generalized stability of complete theories. This paper discusses some problems that are related to the \( P \)-stability of certain classes of \( S \)-acts. In particular, we describe the monoids \( S \) over which the classes of free, projective, strongly flat, divisible, regular \( S \)-acts are \( P \)-stable.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Palyutin E. A., “\( E^{*} \)-Stable theories,” Algebra and Logic, vol. 42, no. 2, 112–120 (2003).

    Article  MathSciNet  Google Scholar 

  2. Palyutin E. A., “\( P \)-Stable Abelian groups,” Algebra and Logic, vol. 52, no. 5, 404–421 (2013).

    Article  MathSciNet  Google Scholar 

  3. Rusaleev M. A., “Characterization of \( (P,1) \)-stable theories,” Algebra and Logic, vol. 46, no. 2, 188–194 (2007).

    Article  MathSciNet  Google Scholar 

  4. Ptakhov D. O., “Polygons with a \( (P,1) \)-stable theory,” Algebra and Logic, vol. 56, no. 6, 473–478 (2017).

    Article  MathSciNet  Google Scholar 

  5. Kilp M., Knauer U., and Mikhalev A. V., Monoids, Acts and Categories, De Gruyter, Berlin and New York (2000).

    Book  Google Scholar 

  6. Mikhalev A. V., Ovchinnikova E. V., Palyutin E. A., and Stepanova A. A., “Model-theoretic properties of regular polygons,” J. Math. Sci. (New York), vol. 140, no. 2, 250–285 (2007).

    Article  MathSciNet  Google Scholar 

  7. Stepanova A. A. and Ptakhov D. O., “\( P \)-Stable polygons,” Algebra and Logic, vol. 56, no. 4, 324–336 (2017).

    Article  MathSciNet  Google Scholar 

  8. Chang C. C. and Keisler H. J., Model Theory, North-Holland, Amsterdam and London (1973).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Far Eastern Federal University, Vladivostok, Russia

    E. N. Stepanova & A. I. Krasitskaya

Authors
  1. E. N. Stepanova
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. I. Krasitskaya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to E. N. Stepanova.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2021, Vol. 62, No. 2, pp. 441–449. https://doi.org/10.33048/smzh.2021.62.214

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Stepanova, E.N., Krasitskaya, A.I. \( P \)-Stability of Some Classes of \( S \)-Acts. Sib Math J 62, 357–363 (2021). https://doi.org/10.1134/S0037446621020142

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0037446621020142

Keywords

UDC

Search

Navigation