IJPAM: Volume 77, No. 4 (2012)
Faculty of Computer Science and System Engineering
Okayama Prefectural University
Soja, 719-1197, JAPAN
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.
Dedicated to Professor Masami Ito
on his 70th birthday.
Received: March 8, 2012
AMS Subject Classification: 16W25
Key Words and Phrases: differential operator, separable extension, Posner's theorem
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395