IJPAM: Volume 30, No. 3 (2006)

A NOTE ON GENERALIZED $(\sigma, \tau)$-DERIVATIONS
ASSOCIATE WITH HOCHSCHILD 2- $(\sigma, \tau)$
COCYCLES OF RINGS

Emine Albas
Department of Mathematics
Faculty of Science
Ege University
Bornova, Izmir, 35100, TURKEY
e-mail: emine.albas@ege.edu.tr


Abstract.Let $R$ be a ring, $M$ an $R$-bimodule, $\sigma$ and $\tau$ endomorphisms of $R$, and $\alpha: R\times R \to M$ a biadditive map. In present paper we introduce a new type of generalized derivations associate with Hochschild 2- $(\sigma, \tau)$ cocycles $\alpha$ and prove that generalized $(\sigma, \tau)$-Jordan derivations of this type are also generalized $(\sigma, \tau)$-derivations under certain conditions.

Received: June 21, 2006

AMS Subject Classification: 16W10, 16W25, 16E40

Key Words and Phrases: derivation, Hochschild 2-cocycle, 2- $(\sigma, \tau)$-cocycles generalized $(\sigma, \tau)$-derivation, generalized $(\sigma, \tau)$-Jordan derivation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 3