ON LIE IDEALS AND GENERALIZED DERIVATIONS OF *-PRIME RINGS


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Huang S., GÖLBAŞI Ö.

MISKOLC MATHEMATICAL NOTES, cilt.14, ss.941-950, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 14 Konu: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.18514/mmn.2013.689
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Sayfa Sayıları: ss.941-950

Özet

Let (r, *) be a 2-torsion free *-prime ring with involution * and center Z (R), U a nonzero square closed *-Lie ideal of R. An additive mapping F W R! R is called a generalized derivation if there exits a derivation d WR R such that F. xy/DF. x/yCxd. y/. In the present paper, we prove that U * Z. R/if any one of following conditions holds: 1) O F. u/; u _ D 0; 2) O d. u/; F. v/_ D 0; 3) d. u/oF. v/D 0; 4) O d. u/; F. v/ D * O u; v; 5) d. u/oF (v) D * uov; 6) d. u/F. v/* uv 2 Z. R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that the *-primeness hypothesis is not superfluous.