共查询到20条相似文献,搜索用时 15 毫秒
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S. K. Tiwari 《代数通讯》2013,41(12):5356-5372
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Let R be a prime ring of char R ≠ 2 with a nonzero derivation d and let U be its noncentral Lie ideal. If for some fixed integers n
1 ⩾ 0, n
2 ⩾ 0, n
3 ⩾ 0, (u
n1 [d(u), u]u
n2)
n3 ∈ Z(R) for all u ∈ U, then 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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Basudeb Dhara 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):401-410
Let R be a prime ring of char R ≠ = 2 with center Z(R) and with extended centroid C, d a nonzero derivation of R and f(x
1, ..., x
n
) a nonzero multilinear polynomial over C. Suppose that x
s
d(x)x
t
∈ Z(R) for all x ∈ {d(f(x
1, ..., x
n
))|x
1, ..., x
n
∈ ρ}, where ρ is a nonzero right ideal of R and s ≥ 0, t ≥ 0 are fixed integers. If d(ρ)ρ ≠ = 0, then ρ
C = eRC for some idempotent e in the socle of RC and f(x
1, ..., x
n
)
N
is central-valued in eRCe, where N = s + t + 1.
相似文献
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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 with center Z(R), I a nonzero ideal of R, d a nonzero derivation of R and 0≠a∈ R. In the present paper, our object is to study the situation a[d(xk), xk]n∈ Z(R) for all x ∈ I under certain conditions, where n(≥ 1), k(≥ 1) are fixed integers. 相似文献
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素环上导子的线性组合 总被引:1,自引:0,他引:1
In this paper we discuss the linear combination of derivations in prime rings which was initiated by Niu Fengwen.Our aim is to improve Niu‘s result.For the proof of the main theorem we generalize a result of Bresar and obtain a lemma that is of independent interest. 相似文献
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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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Let R be a reduced ring with Q its Martindale symmetric ring of quotients, and let B be the complete Boolean algebra of all idempotents in C, where C is the extended centroid of R. It is proved that every minimal prime ideal of R must be of the form mQ∩R for some maximal ideal m of B but the converse is in general not true. In addition, if R is centrally closed or has only finitely many minimal prime ideals, then the converse also holds. By applying the explicit expression, many properties of minimal prime ideals of reduced rings are realized more easily. 相似文献
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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 prime ring with a non-central Lie ideal L. In the present paper we show that if the composition DG of two generalized derivations D and G is zero on L, then DG must be zero on R. And we get all the possibilities for the composition of a couple of generalized derivations to be zero on a non-central Lie ideal of a prime ring. 相似文献
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The concept of derivations and generalized inner derivations has been generalized as an additive function δ: R→ R satisfying δ(xy) = δ(x)y xd(y) for all x,y∈R,where d is a derivation on R.Such a function δis called a generalized derivation.Suppose that U is a Lie ideal of R such that u2 ∈ U for all u ∈U.In this paper,we prove that U(C)Z(R) when one of the following holds:(1)δ([u,v]) = uov (2)δ([u,v]) uov=O(3)δ(uov) =[u,v](4)δ(uov) [u,v]= O for all u,v ∈U. 相似文献
20.
Let R be a prime ring with center Z and S (?) R. Two mappings D and G of R into itself are called cocentralizing on S if D(x)x-xG(x) ∈ Z for all x ∈ S. The main purpose of this paper is to describe the structure of generalized derivations which are cocentralizing on ideals, left ideals and Lie ideals of a prime ring, respectively. The semiprime case is also considered. 相似文献