On Jordan ideals and Jordan derivations of prime rings

• Autorzy: Ashrat M. , Rehman N.
• Języki publikacji: EN

Abstrakty

EN

Let R be a 2-torsion free prime ring, and let J be a nonzero Jordan ideal and a subring of R. In the present paper it is shown that if d is an additive mapping of R into itself satisfying d(u2) = d(u)u + ud(u), for all u 6 J, then d(uv) = d(u)v + ud(v), for all u, v J.

Słowa kluczowe

EN

Jordan ideals; Jordan derivations; derivations; prime rings; torsion free rings

PL

ideały Jordana; pochodne Jordana; pochodne; pierwsze pierścienie

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 3
• Strony: 517--523
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Ashrat M.

• Department of Mathematics, Faculty of Science, King Abdul Aziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

autor

Rehman N.

• Mathematics Group, Birla Institute of Technology & Science, Pilani (Rajasthan) - 333031, India

Bibliografia

• [1] M. Ashraf and N. Rehman, Lie ideals and Jordan left derivations of prime rings, Arch. Math. (Brno) 36 (2000), 1-6.
• [2] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc. 90 (1984), 9-14.
• [3] M. Bresar, Jordan derivations on semiprime rings, Proc. Amer. Math. Soc. 104 (1988), 1003-1006.
• [4] M. Bresar and J. Vukman, Jordan derivations of prime rings, Bull. Aust. Math. Soc. 37 (1988), 321-322.
• [5] M. Bresar and J. Vukman, Jordan (θ,Φ)-derivations, Glasnik Mat. 26 (1991), 13-17.
• [6] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.
• [7] I. N. Herstein, Topics in Ring Theory, Univ. of Chcago Press, Chicago 1969.
• [8] V. K. Kharchenko, Automorphisms and Derivations of Associative Rings, Kluwer Academic Publishers, Dordrecht, Vol. 69, 1991.
• [9] E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957), 1093-1100.