Glasnik Matematicki, Vol. 45, No.1 (2010), 43-53.

ON (m, n)-JORDAN CENTRALIZERS IN RINGS AND ALGEBRAS

Joso Vukman

Abstract.   Let m ≥ 0, n ≥ 0 be fixed integers with m+n ≠ 0 and let R be a ring. It is our aim in this paper to investigate additive mapping T : R → R satisfying the relation (m+n)T(x²) = mT(x)x + nxT(x) for all x R.

2000 Mathematics Subject Classification.   16W10, 46K15, 39B05.

Key words and phrases.   Ring, prime ring, semiprime ring, Banach space, Hilbert space, algebra of all bounded linear operators, standard operator algebra, H*-algebra, derivation, Jordan derivation, left (right) centralizer, two-sided centralizer, left (right) Jordan centralizer, (m,n)-Jordan centralizer.

DOI: 10.3336/gm.45.1.04

References:

1. W. Ambrose, Structure theorems for a special class of Banach algebras, Trans. Amer. Math. Soc. 57 (1945), 364-386.
   MathSciNet     CrossRef

2. K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with generalized identities, Marcel Dekker, Inc., New York, 1996.
   MathSciNet

3. M. Bresar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 37 (1988), 321-323.
   MathSciNet     CrossRef

4. M. Bresar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
   MathSciNet     CrossRef

5. M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), 218-228.
   MathSciNet     CrossRef

6. M. Bresar and B. Hvala, On additive maps of prime rings, II, Publ. Math. Debrecen 54 (1999), 39-54.
   MathSciNet

7. J. Cusack, Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324.
   MathSciNet     CrossRef

8. I. N. Herstein, Jordan derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.
   MathSciNet     CrossRef

9. L. Molnár, On centralizers of an H*-algebra, Publ. Math. Debrecen 46 (1995), 89-95.
   MathSciNet

10. I. Kosi-Ulbl and J. Vukman, On centralizers of standard operator algebras and semisimple H*-algebras, Acta Math. Hungar. 110 (2006), 217-223.
    MathSciNet     CrossRef

11. J. Vukman, An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolin. 40 (1999), 447-456.
    MathSciNet

12. J. Vukman and I. Kosi-Ulbl, Centralizers on rings and algebras, Bull. Austral. Math. Soc. 71 (2005), 225-234.
    MathSciNet     CrossRef

13. J. Vukman and I. Kosi-Ulbl, On centralizers of semisimple H*-algebras, Taiwanese J. Math. 11 (2007), 1063-1074.
    MathSciNet

14. B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolin. 32 (1991), 609-614.
    MathSciNet