Skip to main content
SpringerLink
Log in

Strongly prime alternative pairs with minimal inner ideals

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this paper, we use the known classification of the finite capacity simple alternative pairs and the version of the Litoff Theorem for Jordan pairs to describe all the strongly prime alternative pairs with nonzero socle. We study the inheritance of some properties (primeness, nondegenerancy,…) when passing from the original alternative pair to the symmetrized pair. Thus, we can apply Jordan theoretical results to the alternative case.

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. A. Castellón Serrano and C. Martín González.Prime Alternative Triple Systems. In Non-Associative Algebra and its Applications. Santos González, Ed. Kluwer Academic Publishers. 73–79 (1994)

  2. A. Castellón and J. A. Cuenca.Alternative H *-triple systems, Comm. in Alg. 20(11), 3191–3206 (1992)

    MATH  Google Scholar 

  3. A. Castellón, A. García and C. Martín.Strongly Prime Alternative Triple Systems with Nonzero Socle. Preprint.

  4. J.A. Cuenca Mira, A. García Martín and C. Martín González.Jacobson Density for Associative Pairs and its applications. Comm. in Alg., 17(10), 2595–2610 (1989)

    MATH  Google Scholar 

  5. A. Fernández López, E. García Rus.Prime associative triple systems with nonzero socle. Comm. in Alg. 18(1), 1–13 (1990)

    MATH  Google Scholar 

  6. A. Fernández López, E. García Rus and E. Sánchez Campos,Von Neumann Regular Jordan Banach Triple Systems. J. London Math. Soc. (2) 42 (1990), 32–48.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Fernández López, E. García Rus and E. Sánchez Campos.Prime Nondegenerate Jordan Triple Systems with Minimal Inner Ideals. Nova Science Publishers Inc. (1992) 143–166

  8. N. Jacobson.Structure of Rings. Colloquium Publications 37. American Mathematical Society, Providence, R.I. (1984).

    Google Scholar 

  9. O. Loos,Alternative Tripelsysteme. Math. Ann. 198, 205–238 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  10. O. Loos,Jordan Pairs. Lecture Notes in Mathematics. Springer-Verlag, Berlin-Heidelberg-New York, Vol. no. 460, 1975

    MATH  Google Scholar 

  11. O. Loos.On the socle of a Jordan pair. Collect. Math. 40, 2 (1989), 109–125

    MATH  MathSciNet  Google Scholar 

  12. O. Loos.Finiteness conditions in Jordan pairs. Math. Z. 206, 577–587 (1981)

    MathSciNet  Google Scholar 

  13. K. McCrimmon.Strong prime inheritance in Jordan systems, Alg., Groups and Geometries 1, 217–234 (1984)

    MATH  MathSciNet  Google Scholar 

  14. K. Meyberg.Lectures on Algebras and Triple Systems. Lecture Notes, The University of Virginia, Charlottesville, (1972)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Álgebra, Geometría y Topología Facultad de Ciencias, Universidad de Málaga, Aptdo. 59, 29071, Málaga, España

    Alberto Castellón Serrano, Antonio Fernández López & Cándido Martín González

  2. Departamento de Matemática Aplicada E.T.S.I.I., Universidad de Málaga, 29013, Málaga, España

    Amable García Martín

Authors
  1. Alberto Castellón Serrano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Antonio Fernández López
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Amable García Martín
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cándido Martín González
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This work has been partially supported by 1) the “Plan Andaluz de Investigación y Desarrollo Tecnológico” with project no. 1027 and 2) the DGICYT with project no. PB93-0990

Rights and permissions

Reprints and permissions

About this article

Cite this article

Serrano, A.C., López, A.F., Martín, A.G. et al. Strongly prime alternative pairs with minimal inner ideals. Manuscripta Math 90, 479–487 (1996). https://doi.org/10.1007/BF02568320

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568320

Keywords

Search

Navigation