manuscripta mathematica

, Volume 95, Issue 1, pp 79–90 | Cite as

Towards a goldie theory for jordan pairs

  • Antonio Fernández López
  • Eulalia García Rus
  • Omar Jaa


A Goldie theory for Jordan pairs is started in this paper. We introduce a notion of order in linear Jordan pairs and study orders in nondegenerate linear Jordan pairs with descending chain condition on principal inner ideals.


Jordan Algebra Local Algebra Finite Capacity Ascend Chain Condition Descend Chain Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A. D’Amour and K. McCrimmon,The local algebra of a Jordan system, J. Algebra177, pp. 199–239 (1995).zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    P.N. Anh and L. Marki,Left orders in regular rings with minimum condition for principal one-sided ideals, Math. Proc. Camb. Phil. Soc.109, pp. 323–333 (1991).zbMATHCrossRefGoogle Scholar
  3. [3]
    J.A. Anquela, T. Cortés, O. Loos and K. McCrimmon,An elemental characterization of strong primeness in Jordan systems, J. Pure and Applied Algebra109, pp. 23–36 (1996).zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    D.J. Britten,On prime Jordan rings H(R) with chain condition, J. Algebra178, pp. 414–421 (1973).CrossRefMathSciNetGoogle Scholar
  5. [5]
    D.J. Britten,On semiprime Jordan rings H(R) with acc, Proc. Amer. Math. Soc.45, pp. 175–178 (1974).zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A. Fernández López and E. García Rus,Prime Jordan algebras satisfying local Goldie conditions, J. Algebra74, pp. 1024–1048 (1995).CrossRefGoogle Scholar
  7. [7]
    A. Fernández López and E. García Rus,Nondegenerate Jordan algebras satisfying local Goldie conditions, J. Algebra182, pp. 52–59 (1996).zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    A. Fernández López, E. García Rus, M. Gómez Lozano, and M. Siles Molina,Goldie theorems for associative pairs (to appear).Google Scholar
  9. [9]
    A. Fernández López, E. García Rus and O. Loos,Annihilators of elements of the socle of a Jordan algebra, Comm. in Algebra22, pp. 1729–1740 (1994).zbMATHCrossRefGoogle Scholar
  10. [10]
    J. Fountain and V. Gould,Orders in rings without identity, Comm. in Algebra18, pp. 3085–3110 (1990).zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    J. Fountain and V. Gould,Orders in regular rings with minimal condition for principal right ideals, Comm. in Algebra19, pp. 1501–1527 (1991).zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    N. Jacobson,Structure and representations of Jordan algebras, Colloquium Publications, Vol39, Amer. Math. Soc., Providence (1968).zbMATHGoogle Scholar
  13. [13]
    N. Jacobson, K. McCrimmon and M. Parvathi,Localization of Jordan algebras, Commun. in Algebra6, pp. 911–958 (1978).zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    O. Loos,Jordan pairs, Lecture Notes in Mathematics, Vol460, Springer Berlin-Heidelgeberg-New York (1975).zbMATHGoogle Scholar
  15. [15]
    O. Loos,On the socle of a Jordan pair, Collect. Math.40, pp. 109–125 (1989).zbMATHMathSciNetGoogle Scholar
  16. [16]
    O. Loos,Diagonalization in Jordan pairs, J. Algebra143, pp. 252–268 (1991).zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    K. McCrimmon,Peirce ideals in Jordan triple systems, Pacific J. Math.83, pp. 415–439 (1979).zbMATHMathSciNetGoogle Scholar
  18. [18]
    K. McCrimmon,Strong prime inheritance in Jordan systems, Algebras, Groups and Geometries1, pp. 217–234 (1984).zbMATHMathSciNetGoogle Scholar
  19. [19]
    E. Zelmanov,Goldie’s theorem for Jordan algebras, Siberian Math. J.28, pp. 44–52 (1987).MathSciNetGoogle Scholar
  20. [20]
    E. Zelmanov,Goldie’s theorem for Jordan algebras II, Siberian Math. J.29, pp. 68–74 (1988).MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Antonio Fernández López
    • 1
  • Eulalia García Rus
    • 1
  • Omar Jaa
    • 2
  1. 1.Departamento de Algebra, Geometría y Topología, Facultad de CienciasUniversidad de MálagaMálagaSpain
  2. 2.Département de Mathématiques et InformatiqueUniversité Chouaib Doukkali, Faculté des SciencesEl Jadida, Morroco

Personalised recommendations