# On Extension and Structure of Generalized Derivations

### New Zealand Journal of Mathematics

Vol. 42, (2012), Pages 83-90

Carlos Peña

UNCPBA,

NUCOMPA

Abstract We are concerned with the extension problem and the nature of ge-neralized derivations of an underlying associative algebra $\mathcal{A}$ on a field k to the corresponding double centralizer algebra and to the unitized algebra. This investigation will be made in the frame of some general associative algebras. We shall also seek on the continuity of generalized derivations on normed algebras.

Keywords Semiprime ring, separating space of a linear map.

Classification (MSC2000) Primary: 16W25, Secondary: 47B47