Sugli anelli ternari di Hestenes

  • Antonino Giorgio Spera


We study Hestenes rings (H-rings)R and we give a characterization of the Jacobson radicalJ(R). We prove that ifR is semisimple thenR is a subdirect sum of quasi-primitive H-rings, and that ifR has D.C.C. on right ideals thenJ(R) is nilpotent and every nil right ideals ofR lies inJ(R). Moreover we show that ifR is a H-ring with A.C.C. on right (left) ideals, then every nil right ideal is nilpotent and avery nil left ideal is nilpotent.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bartolozzi F. e Panella G.,Anelli ternari di Hestenes semplici artiniani e privi di ideali bilateri effettivi, Ricerche di Mat.,26 (1977), 255–275.MathSciNetGoogle Scholar
  2. [2]
    Bergman G.,A ring primitive on the right but not on the left, Proc. Amer. Math. Soc.,15 (1964), 473–475.MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Divinsky N. J.,Rings and Radicals, George Allen and Unwin LTD, London, 1965.MATHGoogle Scholar
  4. [4]
    Herstein J. N.,Non commutative rings, Carus Math. Monographs, 1968.Google Scholar
  5. [5]
    Loos O.,Assoziative Tripelsysteme, Manuscripta Math.,7 (1972), 103–112.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Profera L.Anelli ternari di Hestenes semplici e artiniani, Atti Acc. Naz. Lincei, Rend. Cl. Sc. fis. mat e nat.,62 (1977), 292–299.MATHMathSciNetGoogle Scholar
  7. [7]
    Spera, A. G.,Radicale di un anello di Hestenes, Atti Acc. Sc. Lett. e Arti Palermo Parte 1,35 (1975–76), 283–296.MathSciNetGoogle Scholar
  8. [8]
    Stephenson R. A.,Jacobson structure theory for Hestenes ternary rings, Trans. Amer. Math. Soc.,177 (1973), 91–98.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer 1978

Authors and Affiliations

  • Antonino Giorgio Spera
    • 1
  1. 1.Belmonte Mezzagno(Palermo)

Personalised recommendations