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Content available remote Semiprime near-rings with multiplicative generalized (θ,θ)-derivations
Let N be a semiprime right near-ring and I a semigroup ideal of N. A map f : N →N is called a multiplicative generalized (θ,θ)-derivation if there exists a multiplicative (θ,θ)-derivation d : R → such that f(xy) - f(x)θ(y) + θ(x)d(y), for all x,y ϵ R. The purpose of this paper is to investigate the following: [formula].
We apply a fixed point theorem to prove that there exists a unique derivation close to an approximately generalized derivation in Lie C*-algebras. Also, we prove the hyperstability of generalized derivations. In other words, we find some conditions under which an approximately generalized derivation becomes a derivation.
Let R be a prime ring with Utumi quotient ring U and with extended centroid C, I a non-zero right ideal of R, f(x1,…,xn) a multilinear polynomial over C which is not central valued on R and G, H two generalized derivations of R. Suppose that G(f(r))f(r) – f(r)H(f(r)) € C, for all r = (r1,…,rn) € In. Then one of the following holds: 1. there exist a; b; p (…) ; 2. R satisfies s4, the standard identity of degree 4, and there exist a; (…) ; 3. R satisfies s4 and there exist a; (…) ; 4. R satisfies s4 and there exist a; (…) ; 5. there exists e2 = e (…) and one of the following holds: (a) (…) is an identity for I; (b) char(R) = 2 and s4(x1, x2, x3, x4)x5 is an identity for I; (c) (…) is an identity for I and there exist a, a’, b, b’ (…) , a derivation of R, such that G(x) = ax + xa’ + d(x), H(x) = bx + xb’ – d(x), for all x (…) R, with (a – b’ – α)I = (0) = (b – a’ – α)I.
Content available remote Identities with generalized derivations in semiprime rings
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.
Content available remote Generalized finite operators
Let B(H) be the algebra of all bounded linear operators on an infinite dimensional complex and separable Hilbert space H. A infinity B(H) is called finite if \\AX - XA - I\\ > 1, VX infinity B(H). In this paper we extend the class of finite operators to a more general class of pairs of operators called generalized finite operators defined by {(A, B) infinity B(H) x B(H) : \\AX - XB - I\\ > 1, VX infinity B(H)} and we present some pairs of generalized finite operators.
Content available remote Finite operators
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