Jordan Derivations and Antiderivations of Generalized Matrix Algebras
نویسندگان
چکیده
Let G = [ A M N B ] be a generalized matrix algebra defined by the Morita context (A,B,A MB,B NA,ΦMN ,ΨNM) . In this article we mainly study the question of whether there exist the so-called “proper” Jordan derivations for the generalized matrix algebra G . It is shown that if one of the bilinear pairings ΦMN and ΨNM is nondegenerate, then every antiderivation of G is zero. Furthermore, if the bilinear pairings ΦMN and ΨNM are both zero, then every Jordan derivation of G is the sum of a derivation and an antiderivation. Several constructive examples and counterexamples are presented. Mathematics subject classification (2010): 15A78, 16W25, 47L35.
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