Skip to main content
SpringerLink
Log in

On the classification of some classes of Hamiltonian rings

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

The present paper is devoted to the study of some subclasses of H-rings, i.e., rings in which all subrings are ideals. In the description of H-rings an important role is played by almost null rings. We classify, up to isomorphism, torsion almost null rings of bounded exponent.

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. Andrijanov V.I.: Mixed Hamiltonian nilrings. Ural. Gos. Univ. Mat. Zap, 5, 15–30 (1966) (in Russian)

    MathSciNet  Google Scholar 

  2. V. I. Andrijanov, Periodic Hamiltonian rings, Mat. Sb. (N.S.), 74(116) (1967), 241–261 (in Russian); translation in Mat. Sbornik, 74(116) (1967), 225–241.

  3. Andruszkiewicz R.R., Pryszczepko K.: The classification of commutative noetherian, filial rings with identity. Comm. Algebra, 40, 1690–1703 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Andruszkiewicz R.R., Pryszczepko K.: The classification of commutative torsion filial rings. J. Aust. Math. Soc., 95, 289–296 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Andruszkiewicz and K. Pryszczepko, On the non-torsion almost null rings, Recent Results in Pure and Applied Mathematics, Białystok Technical University Publishing Office (2014).

  6. Andruszkiewicz R.R., Pryszczepko K.: Adjoining an identity to a finite filial ring. New York J. Math., 20, 695–710 (2014)

    MathSciNet  MATH  Google Scholar 

  7. Antipkin V.G., Elizarov V.P.: Rings of order p 3. Sib. Mat. Zhurnal, 23, 9–18 (1982)

    MATH  Google Scholar 

  8. Freidman P.A.: Letter to the editors. Mat. Sb., 52(94), 915–916 (1960) (in Russian)

    MathSciNet  Google Scholar 

  9. L. Fuchs, Infinite Abelian Groups, vol. 1, Academic Press (London, 1970).

  10. A. Jones and J. J. Schäffer, Concerning the structure of certain rings, Bol. Fac. Ingen. Agriment., 6 (1957–1958), 327–335.

  11. R. L. Kruse, Rings with periodic additive group in which all subrings are ideals, Dissertation, California Institute of Technology (1964).

  12. Kruse R.L.: Rings in which all subrings are ideals. Canad. J. Math., 20, 862–871 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  13. R. L. Kruse and D. T. Price, Nilpotent Rings, Gordon and Breach, Science Publishers (1969).

  14. H. Prüfer, Unendliche abelsche Gruppen von Elementen endlicher Ordnung, Dissertation (Berlin, 1921).

  15. Rédei L.: Vollidealringe im weiteren Sinn. I. Acta Math. Acad. Sci. Hungar., 3, 243–268 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rédei L.: Die Vollidealringe. Monatsh. Math., 56, 89–95 (1952)

    Article  MathSciNet  MATH  Google Scholar 

  17. Walker E.A.: Cancellation in direct sums of groups. Proc. Amer. Math. Soc., 7, 898–902 (1956)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Białystok, K. Ciołkowskiego 1M, 15-245, Białystok, Poland

    R. R. Andruszkiewicz & K. Pryszczepko

Authors
  1. R. R. Andruszkiewicz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Pryszczepko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Pryszczepko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andruszkiewicz, R.R., Pryszczepko, K. On the classification of some classes of Hamiltonian rings. Acta Math. Hungar. 152, 269–290 (2017). https://doi.org/10.1007/s10474-017-0730-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10474-017-0730-6

Key words and phrases

Mathematics Subject Classification

Search

Navigation