Ograniczanie wyników
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 14

Liczba wyników na stronie   Strona / 1   Wyniki wyszukiwania
Wyszukiwano:
w słowach kluczowych:  semiprime ring Sortuj według: Ogranicz wyniki do:   Strona / 1   1  On Jordan triple α-* centralizers of semiprime rings
EN
Let R be a 2-torsion free semiprime ring equipped with an involution *. An additive mapping T : R → R is called a left (resp. right) Jordan α-* centralizer associated with a function α : R → R if T(x2) = T(x)α(x*) (resp. T(x2) = α(x*)T(x)) holds for all x (…) R. If T is both left and right Jordan α-* centralizer of R, then it is called Jordan α-* centralizer of R. In the present paper it is shown that if α is an automorphism of R, and T : R → R is an additive mapping such that 2T(xyx) = T(x)α(y*x*) + α(x*y*)T(x) holds for all x; y (…) R, then T is a Jordan α-* centralizer of R.
2  On derivations of operator algebras with involution
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.
3  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.
4  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.
5  On (…)-centralizers of semiprime rings
EN
Let R be a semiprime ring with center Z(R) and (…) be a surjective ho-omorphism. In this paper, we prove that T is a (…)-centralizer if one of the following holds: (…).
6  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.
7  Identities with two automorphisms on semiprime rings
EN
In this paper we investigate identities with two automorphisms on semiprime rings. We prove the following result: Let T, S : R approaches R be automorphisms where R is a 2-torsion free semiprime ring satisfying the relation T(x)x = xS(x) for all x is an element of R. In this case the mapping x approaches T(x) - x maps R into its center and T = S.
8  Identities with products of (alpha, beta)-derivations on prime rings
EN
The main purpose of this paper is to prove the following result. Let R be a noncommutative prime ring of characteristic different from two and let D and G = 0 be (\alpha, beta)-derivations of R into itself such that G commutes with alpha and beta. If [D{x), G(x)] = 0 holds for all x is an eleemnt of R then D = lambdaG where lambda is an element from the extended centroid of R.
9  On alfa-derivations of prime and semiprime rings
EN
In this paper we investigate identities with alfa-derivations on prime and semiprime rings. We prove, for example, the following result. If D : R - R is an alfa-derivation of a 2 and 3-torsion free semiprime ring R such that [D(x},x2] = 0 holds, for all x is an element of R, then D maps R into its center. The results of this paper are motivated by the work of Thaheem and Samman .
10  Free actions of semiprime rings with involution induced a derivation
EN
Let R be an associative ring. An element a is an element of R is said to be dependent of a mapping F : R -> R in case F (x) a = ax holds for all x is an element of R. A mapping F : R -> R is called a free action in case zero is the only dependent element of F. In this paper free actions of semiprime *- rings induced by a derivation are considered. We prove, for example, that in case we have a derivation D : R -> R, where R is a semiprime *-ring, then the mapping F defined by F(x) = D(x*) + D(x)*,x is an element of R, is a free action. It is also proved that any Jordan *-derivation on a 2-torsion free semiprime *-ring is a free action.
11  A note centralizers in semiprime rings
EN
The purpose of this paper is to prove the following result: Let R be a (m+n + 2)! and 3m2n + 3mn2 + 4m2 + 4n2 +10mn-torsion free semiprime ring with an identity element and let T : R -R be an additive mapping such that 3T(xm+n+1) = T(x)xm+n + xmT(x)xn + xm=nT(x) is fulfilled for all x is an element R and some fixed nonnegative integers m and n, m+n=0. In this case T is a centralizer.
12  On (α, β)-derivations of semiprime rings, II
13  Centralizing mappings and derivations on semiprime rings
EN
In this paper we study some properties of centralizing mappings on semi-prime rings. The main purpose is to prove the result: Let -R be a semiprime ring and f an endomorphism of R, g an epimorphism of R such that the mapping x -> [f(x),g(x)] is central. Then [f(x),g(x)] = 0 holds for all x e R. We also establish some results about (alpha,beta)-derivations.
14  A note on (alpha)-derivations on semiprime rings
EN
In this note we investigate some properties of a-derivations on prime and semiprime rings. We establish some identities for a commuting a-derivation d on a semiprime ring R and show that d maps R into its center and obtain some well-known results as a consequence. We also generalize Posner's theorem on the composition of derivations for a-derivations and as an application resolve a functional equation of automorphisms on certain prime rings.   Strona / 1    JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.