共查询到20条相似文献,搜索用时 11 毫秒
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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 for all r1,..., r n ∈ R. Then d and g are both inner derivations on R and one of the following holds: (1) d = g = 0; (2) d = ?g and f(x 1,..., x n )2 is central-valued on R.
相似文献
$\delta (d(f(r_1 , \ldots ,r_n ))f(r_1 , \ldots ,r_n ) - f(r_1 , \ldots ,r_n )g(f(r_1 , \ldots ,r_n ))) = 0$
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S. K. Tiwari 《代数通讯》2013,41(12):5356-5372
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Chen-Lian Chuang 《代数通讯》2017,45(7):2837-2847
Let R be a prime ring and δ a σ-derivation of R, where σ is an automorphism of R. Our aim (Theorem 1) is to determine any automorphism S of R[t;σ,δ] satisfying S(A)?R for a one-sided ideal A≠0 of R by dropping the assumption t∈R[t;σ,δ]. As an application, if R is a domain, it is shown that any X-inner automorphism of R[t;σ,δ] stabilizes R. 相似文献
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Nihan Baydar Yarbil 《代数通讯》2018,46(1):205-216
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Let R be a prime ring of char R ≠ 2, let d be a nonzero derivation of R, and let ρ be a nonzero right ideal of R such that [[d(x)x n , d(y)] m , [y, x] s ] t = 0 for all x, y ? ρ, where n ≥ 1, m ≥ 0, s ≥ 0, and t ≥ 1 are fixed integers. If [ρ, ρ]ρ ≠ 0 then d(ρ)ρ = 0. 相似文献
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Let R be a prime ring of characteristic different from 2, U its right Utumi quotient ring, C its extended centroid and L a not central Lie ideal of R. Suppose that F, G and H are generalized derivations of R, with F≠0, such that F(G(x)x?xH(x)) = 0, for any x∈L. In this paper we describe all possible forms of F, G and H. 相似文献
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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
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Joso Vukman 《Acta Mathematica Hungarica》2006,112(3):181-186
Summary Let X be a complex Hilbert space, let L(X) be the 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 D(AA*A) = D(A) A*A + AD(A*)A + AA*D(A), for all A ∈ A(X). In this case D is of the form D(A) = AB-BA, for all A∈ A(X) and some B ∈ L(X), which means that D is a derivation. We apply this result to semisimple H*-algebras. 相似文献
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Tsiu-Kwen Lee 《代数通讯》2019,47(1):236-251
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On approximately higher ring derivations 总被引:1,自引:0,他引:1
In this paper, we examine the Hyers-Ulam, the Isac and Rassias-type stability and the Bourgin-type superstability of a functional inequality corresponding to the following functional equation, respectively:
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Let R be a ring with a subset S. A mapping of R into itself is called strong commutativitypreserving (scp) on S, if [f(x), f(y)] = [x, y] for all x, y ∈ S. The main purpose of this paper is to describe the structure of the generalized derivations which are scp on some ideals and right ideals of a prime ring, respectively. The semiprime case is also considered. 相似文献
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