[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2016.56.2.397

Derivations with Power Values on Lie Ideals in Rings and Banach Algebras

Rehman, Nadeem ur (Department of Mathematics, Faculty of Science, Taibah University)
Muthana, Najat Mohammed (Department of Mathematics, Science Faculty for Girls, King Abdulaziz University)
Raza, Mohd Arif (Department of Mathematics, Aligarh Muslim University)

Publication Information

Kyungpook Mathematical Journal / v.56, no.2, 2016 , pp. 397-408 More about this Journal

Abstract

Let R be a 2-torsion free prime ring with center Z, U be the Utumi quotient ring, Q be the Martindale quotient ring of R, d be a derivation of R and L be a Lie ideal of R. If $d(uv)^n=d(u)^md(v)^l$ or $d(uv)^n=d(v)^ld(u)^m$ for all $u,v{\in}L$ , where m, n, l are xed positive integers, then $L{\subseteq}Z$ . We also examine the case when R is a semiprime ring. Finally, as an application we apply our result to the continuous derivations on non-commutative Banach algebras. This result simultaneously generalizes a number of results in the literature.

Keywords

Prime and semiprime rings; Derivations; Martindale ring of quotients; Banach algebras; Radical;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

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