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EN
The purpose of this paper is to prove the following result. Let X be a complex Hilbert space, let L(X) be an algebra of all bounded linear operators on X and let A(X) (…) L(X) be a standard operator algebra, which is closed under the adjoint operation. Suppose there exists a linear mapping D : A(X) → L(X) satisfying the relation 2D(AA*A) = D(AA*)A + AA*D(A) + D(A)A*A + AD(A*A) for all A (…) A(X). In this case, D is of the form D(A) = [A,B] for all A (…) A(X) and some fixed B (…) L(X), which means that D is a derivation.
2  Identities with generalized derivations in semiprime rings
EN
Let R be a semiprime ring. An additive mapping F:R  R is called a generalized derivation of R if there exists a derivation d : R  R such that F(xy) = F(x)y + xd(y) holds, for all x,y  R. The objective of the present paper is to study the following situations: (1) (...), for all x, y in some appropriate subset of R.
3  A note on generalized (m, n)-Jordan centralizers
EN
The aim of this paper is to define generalized (m, n)-Jordan centralizers and to prove that on a prime ring with nonzero center and char (R) ≠ 6mn(m+n)(m+2n) every generalized (m, n)-Jordan centralizer is a two-sided centralizer.
4  Jordan structure on prime rings with centralizers
EN
Our object in this paper is to study the generalization of Borut Zalar result in  on Jordan centralizer of semiprime rings by prove the following result: Let R be a prime of characteristic different from 2, and U be a Jordan ideal of R. If T is an additive mapping from R to itself satisfying the following condition T(ur + ru) = uT(r) + T(r)u, then T(ur) = uT(r), for all r is an element of R, u is an element of U.   Strona / 1    JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.