A NOTE ON JORDAN DERIVATIONS OF TRIVIAL GENERALIZED MATRIX ALGEBRAS

On Jordan left derivations and generalized Jordan left derivations of matrix rings

Abstract. Let R be a 2-torsion free ring with identity. In this paper, first we prove that any Jordan left derivation (hence, any left derivation) on the full matrix ringMn(R) (n 2) is identically zero, and any generalized left derivation on this ring is a right centralizer. Next, we show that if R is also a prime ring and n 1, then any Jordan left derivation on the ring Tn(R) of all n×n uppe...

Jordan Derivations and Antiderivations of Generalized Matrix Algebras

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 ...

Generalized Derivations and Bilocal Jordan Derivations of Nest Algebras

Jordan automorphisms, Jordan derivations of generalized triangular matrix algebra

Derivations, Jordan derivations, as well as automorphisms and Jordan automorphisms of the algebra of triangular matrices and some class of their subalgebras have been the object of active research for a long time [1, 2, 5, 6, 9, 10]. A well-know result of Herstein [11] states that every Jordan isomorphism on a prime ring of characteristic different from 2 is either an isomorphism or an anti-iso...

on jordan left derivations and generalized jordan left derivations of matrix rings

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...