Original scientific paper

Identities with derivations on rings and Banach algebras

Joso Vukman

Abstract

In this paper we prove the following result. Let m 1, n 1 be integers and let R be a 2mn(m+n-1)!-torsion free semiprime ring. Suppose there exist derivations D, G : R R such that D(xm)xn + xnG(xm) = 0 holds for all x R. In this case both derivations D and G map R into its center and D = -G. We apply this purely algebraic result to obtain a range inclusion result of continuous derivations on Banach algebras.

Keywords

Prime ring; semiprime ring; Banach algebra; derivation; commuting mapping; centralizing mapping; skew-commuting mapping; skew-centralizing mapping

Hrčak ID:

373

URI

https://hrcak.srce.hr/373

Publication date:

9.11.2005.

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