共查询到20条相似文献,搜索用时 15 毫秒
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In this paper we investigate identities with two generalized derivations in prime rings. We prove, for example, the following result. Let R be a prime ring of characteristic different from two and let F 1, F 2 : R → R be generalized derivations satisfying the relation F 1(x)F 2(x) + F 2(x)F 1(x) = 0 for all ${x \in R}$ . In this case either F 1 = 0 or F 2 = 0. 相似文献
3.
Marcin Balcerowski 《Aequationes Mathematicae》2009,78(3):247-255
We solve the equation
f(x+g(y)) - f(y + g(y)) = f(x) - f(y)f(x+g(y)) - f(y + g(y)) = f(x) - f(y) 相似文献
4.
《代数通讯》2013,41(10):4437-4450
Let R be a prime ring with extended centroid C. By a generalized derivation of R we mean an additive map g: R → R such that (xy) g = xgy + xy δ for all x ∈ R, where δ is a derivation of R. In this paper we prove a version of Kharchenko's theorem for generalized derivations and present some results concerning certain identities with generalized derivations. 相似文献
5.
Cheng-Kai Liu 《Monatshefte für Mathematik》2012,166(3-4):453-465
We characterize a prime ring R which admits a generalized derivation g and a map f : ρ → R such that [ f (x), g(y)]?=?[x, y] for all ${x,y\in \rho}$ , where ρ is a nonzero right ideal of R. With this, several known results can be either deduced or generalized. 相似文献
6.
I. N. Herstein [10] proved that a prime ring of characteristic not two with a nonzero derivation d satisfying d(x)d(y) = d(y)d(x) for all x, y must be commutative, and H. E. Bell and M. N. Daif [8] showed that a prime ring of arbitrary characteristic with nonzero derivation d satisfying d(xy) = d(yx) for all x, y in some nonzero ideal must also be commutative. For semiprime rings, we show that an inner derivation satisfying the condition of Bell and Daif on a nonzero ideal must be zero on that ideal, and for rings with identity, we generalize all three results to conditions on derivations of powers and powers of derivations. For example, let R be a prime ring with identity and nonzero derivation d, and let m and n be positive integers such that, when charR is finite, m ∨ n < charR. If d(x m y n ) = d(y n x m ) for all x, y ∈ R, then R is commutative. If, in addition, charR≠ 2 and the identity is in the image of an ideal I under d, then d(x) m d(y) n = d(y) n d(x) m for all x, y ∈ I also implies that R is commutative. 相似文献
7.
Vincenzo De Filippis 《Siberian Mathematical Journal》2009,50(4):637-646
Let R be a prime ring of characteristic different from 2 and extended centroid C and let f(x1,..., x n ) be a multilinear polynomial over C not central-valued on R, while δ is a nonzero derivation of R. Suppose that d and g are derivations of R such that 相似文献
$\delta (d(f(r_1 , \ldots ,r_n ))f(r_1 , \ldots ,r_n ) - f(r_1 , \ldots ,r_n )g(f(r_1 , \ldots ,r_n ))) = 0$ 8.
Vincenzo De Filippis 《Czechoslovak Mathematical Journal》2016,66(2):481-492
Let R be a prime ring of characteristic different from 2 and 3, Qr its right Martindale quotient ring, C its extended centroid, L a non-central Lie ideal of R and n ≥ 1 a fixed positive integer. Let α be an automorphism of the ring R. An additive map D: R → R is called an α-derivation (or a skew derivation) on R if D(xy) = D(x)y + α(x)D(y) for all x, y ∈ R. An additive mapping F: R → R is called a generalized α-derivation (or a generalized skew derivation) on R if there exists a skew derivation D on R such that F(xy) = F(x)y + α(x)D(y) for all x, y ∈ R. 相似文献
9.
Cheng-Kai Liu 《Linear and Multilinear Algebra》2013,61(8):905-915
We apply elementary matrix computations and the theory of differential identities to prove the following: let R be a prime ring with extended centroid C and L a noncommutative Lie ideal of R. Suppose that f?:?L?→?R is a map and g is a generalized derivation of R such that [f(x),?g(y)]?=?[x,?y] for all x,?y?∈?L. Then there exist a nonzero α?∈?C and a map μ?:?L?→?C such that g(x)?=?αx for all x?∈?R and f(x)?=?α?1 x?+?μ(x) for all x?∈?L, except when R???M 2(F), the 2?×?2 matrix ring over a field F. 相似文献
10.
Based on a theorem of McCoy on commutative rings, Nielsen called a ring R right McCoy if, for any nonzero polynomials f(x), g(x) over R, f(x)g(x) = 0 implies f(x)r = 0 for some 0 ≠ r ? R. In this note, we consider a skew version of these rings, called σ-skew McCoy rings, with respect to a ring endomorphism σ. When σ is the identity endomorphism, this coincides with the notion of a right McCoy ring. Basic properties of σ-skew McCoy rings are observed, and some of the known results on right McCoy rings are obtained as corollaries. 相似文献
11.
Cheng-Kai Liu 《Algebras and Representation Theory》2013,16(6):1561-1576
We investigate the commutativity in a (semi-)prime ring R which admits skew derivations δ 1, δ 2 satisfying [δ 1(x), δ 2(y)]?=?[x, y] for all x, y in a nonzero right ideal of R. This result is a natural generalization of Bell and Daif’s theorem on strong commutativity preserving derivations and a recent result by Ali and Huang. 相似文献
12.
Włodzimierz Fechner 《Aequationes Mathematicae》2010,79(3):307-314
The aim of the paper is to deal with the following composite functional inequalities
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