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2. An identity with derivations in prime rings

Author

Shuliang Huang

Subjects
Numerical Analysis, Control and Optimization, Algebra and Number Theory, Identity (philosophy), media_common.quotation_subject, Discrete Mathematics and Combinatorics, Analysis, Linguistics, Prime (order theory), Mathematics, media_common
Published
2018

3. On Lie ideals and generalized derivations of *-prime rings

Author

Shuliang Huang, Öznur Gölbaşi, and [Huang, Shuliang] Chuzhou Univ, Dept Math, Chuzhou 239012, Anhui, Peoples R China -- [Golbasi, Oznur] Cumhuriyet Univ, Fac Sci, Dept Math, TR-58140 Sivas, Turkey

Subjects
Numerical Analysis, Pure mathematics, prime rings, Control and Optimization, Algebra and Number Theory, derivations, Discrete Mathematics and Combinatorics, Lie ideals, generalized derivations, Analysis, Prime (order theory), Mathematics
Abstract

WOS: 000338514500017, 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.

Published
2013

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