Abstract. We define generalized derivations of bimodules over noncommutative rings, which extend the notion of derivations, and construct a module which generates all generalized derivations. Using generalized derivations, we characterize separable ring extensions. We also generalize Posner's theorem on the composition of two derivations of a prime ring to a theorem on generalized derivations.

Received: March 8, 2012

AMS Subject Classification: 16W25

Key Words and Phrases: differential operator, separable extension, Posner's theorem

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