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Basudeb Dhara 《代数通讯》2013,41(6):2159-2167
Let R be a prime ring of char R ≠ 2, d a nonzero derivation of R, U a noncentral Lie ideal of R, and a ∈ R. If au n 1 d(u) n 2 u n 3 d(u) n 4 u n 5 … d(u) n k?1 u n k = 0 for all u ∈ U, where n 1, n 2,…,n k are fixed non-negative integers not all zero, then a = 0 and if a(u s d(u)u t ) n ∈ Z(R) for all u ∈ U, where s ≥ 0, t ≥ 0, n ≥ 1 are some fixed integers, then either a = 0 or R satisfies S 4, the standard identity in four variables. 相似文献
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Let R be a noncommutative prime ring of characteristic different from 2 with Utumi quotient ring U and extended centroid C, and f(x1,…, xn) be a multilinear polynomial over C, which is not central valued on R. Suppose that F and G are two generalized derivations of R and d is a nonzero derivation of R such that d(F(f(r))f(r) ? f(r)G(f(r))) = 0 for all r = (r1,…, rn) ∈ Rn, then one of the following holds:
There exist a, p, q, c ∈ U and λ ∈C such that F(x) = ax + xp + λx, G(x) = px + xq and d(x) = [c, x] for all x ∈ R, with [c, a ? q] = 0 and f(x1,…, xn)2 is central valued on R;
There exists a ∈ U such that F(x) = xa and G(x) = ax for all x ∈ R;
There exist a, b, c ∈ U and λ ∈C such that F(x) = λx + xa ? bx, G(x) = ax + xb and d(x) = [c, x] for all x ∈ R, with b + αc ∈ C for some α ∈C;
R satisfies s4 and there exist a, b ∈ U and λ ∈C such that F(x) = λx + xa ? bx and G(x) = ax + xb for all x ∈ R;
There exist a′, b, c ∈ U and δ a derivation of R such that F(x) = a′x + xb ? δ(x), G(x) = bx + δ(x) and d(x) = [c, x] for all x ∈ R, with [c, a′] = 0 and f(x1,…, xn)2 is central valued on R.
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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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Tsiu-Kwen Lee 《代数通讯》2013,41(2):661-669
ABSTRACT Let R be a prime algebra of characteristic not 2, and let δ be a q-skew σ-derivation of R. We show that if δ2n = 0 and q n ≠ ?1, then δ2n?1 = 0. 相似文献
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Chen-Lian Chuang 《代数通讯》2013,41(2):527-539
Soient D un corps non nécessairement commutatif et L un sous-corps de D. On établit une condition nécessaire et suffisante pour que le groupe multiplicatif L de L soit d'indice fini dans son normalisateur N dans D. Lorsque la dimension à gauche [D : L]g est un nombre premier, on précise le groupe N/L et la structure de D. 相似文献
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Chen-Lian Chuang 《代数通讯》2013,41(2):481-502
Let R be a right Ore domain and φ a derivation or an automorphism of R. We determine the right Martindale quotient ring of the Ore extension R[t; φ] (Theorem 1.1). As an attempt to generalize both the Weyl algebra and the quantum plane, we apply this to rings R such that k[x] ? R ? k(x), where k is a field and x is a commuting variable. The Martindale Quotient quotient ring of R[t; φ] and its automorphisms are computed. In this way, we obtain a family of non-isomorphic infinite dimensional simple domains with all their automorphisms explicitly described. 相似文献
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In this article we prove that the extended centroid of a nondegenerate Jordan system is isomorphic to the centroid (and to the center in the case of Jordan algebras) of its maximal Martindale-like system of quotients with respect to the filter of all essential ideals. 相似文献
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Let R be a semiprime ring with symmetric Martindale quotient ring Q, n ≥ 2 and let f(X) = X n h(X), where h(X) is a polynomial over the ring of integers with h(0) = ±1. Then there is a ring decomposition Q = Q 1 ⊕ Q 2 ⊕ Q 3 such that Q 1 is a ring satisfying S 2n?2, the standard identity of degree 2n ? 2, Q 2 ? M n (E) for some commutative regular self-injective ring E such that, for some fixed q > 1, x q = x for all x ∈ E, and Q 3 is a both faithful S 2n?2-free and faithful f-free ring. Applying the theorem, we characterize m-power commuting maps, which are defined by linear generalized differential polynomials, on a semiprime ring. 相似文献
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Let R be a noncommutative prime ring and d, δ two nonzero derivations of R. If δ([d(x), x] n ) = 0 for all x ∈ R, then char R = 2, d 2 = 0, and δ = αd, where α is in the extended centroid of R. As an application, if char R ≠ 2, then the centralizer of the set {[d(x), x] n | x ∈ R} in R coincides with the center of R. 相似文献
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Tsiu-Kwen Lee 《代数通讯》2013,41(7):2923-2927
Let R be a semiprime ring with Q ml (R) the maximal left ring of quotients of R. Suppose that T: R → Q ml (R) is an additive map satisfying T(x 2) = xT(x) for all x ∈ R. Then T is a right centralizer; that is, there exists a ∈ Q ml (R) such that T(x) = xa for all x ∈ R. 相似文献
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In this paper, we investigate commutativity of ring R with involution ? which admits a derivation satisfying certain algebraic identities. Some well-known results characterizing commutativity of prime rings have been generalized. Finally, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous. 相似文献
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