共查询到20条相似文献,搜索用时 31 毫秒
1.
Vincenzo De Filippis 《Israel Journal of Mathematics》2007,162(1):93-108
Let R be a prime ring with extended centroid C, g a nonzero generalized derivation of R, f (x
1,..., x
n) a multilinear polynomial over C, I a nonzero right ideal of R.
If [g(f(r
1,..., r
n)), f(r
1,..., r
n)] = 0, for all r
1, ..., r
n ∈ I, then either g(x) = ax, with (a − γ)I = 0 and a suitable γ ∈ C or there exists an idempotent element e ∈ soc(RC) such that IC = eRC and one of the following holds:
Supported by a grant from M.I.U.R. 相似文献
(i) | f(x 1,..., x n) is central valued in eRCe |
(ii) | g(x) = cx + xb, where (c+b+α)e = 0, for α ∈ C, and f (x 1,..., x n)2 is central valued in eRCe |
(iii) | char(R) = 2 and s 4(x 1, x 2, x 3, x 4) is an identity for eRCe. |
2.
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
3.
Let K be a commutative ring with unity, R a prime K-algebra, Z(R) the center of R, d and δ nonzero derivations of R, and f(x 1,…, x n ) a multilinear polynomial over K. If [d(f(r 1,…, r n )), δ (f(r 1,…, r n ))] ? Z(R), for all r 1,…, r n ? R, then either f(x 1,…, x n ) is central valued on R or {d, δ} are linearly dependent over C, the extended centroid of R, except when char(R) = 2 and dim C RC = 4. 相似文献
4.
The present paper first establishes a decomposition result for f(x)∈ C
r
C
r+1. By using this decomposition we thus can obtain an estimate of ∣f(x) - L
n
(f,x)∣ which reflects the influence of the position of the x's and ω(f
(r+1),δ)j, j = 0,1,...,s, on the error of approximation.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
5.
A. Kopotowski M G. Nadkarni K. P. S. Bhaskara Rao 《Proceedings Mathematical Sciences》2003,113(1):77-86
We discuss subsetsS of ℝn such that every real valued functionf onS is of the formf(x1, x2, ..., xn) =u
1(x1) +u
2(x2) +...+u
n(xn), and the related concepts and situations in analysis. 相似文献
6.
S. P. Zhou 《Israel Journal of Mathematics》1992,78(1):75-83
The present paper gives a converse result by showing that there exists a functionf ∈C
[−1,1], which satisfies that sgn(x)f(x) ≥ 0 forx ∈ [−1, 1], such that {fx75-1} whereE
n
(0)
(f, 1) is the best approximation of degreen tof by polynomials which are copositive with it, that is, polynomialsP withP(x(f(x) ≥ 0 for allx ∈ [−1, 1],E
n(f) is the ordinary best polynomial approximation off of degreen. 相似文献
7.
Let R be a noncommutative prime ring of characteristic different from 2, let Z(R) be its center, let U be the Utumi quotient ring of R, let C be the extended centroid of R, and let f(x
1,..., x
n
) be a noncentral multilinear polynomial over C in n noncommuting variables. Denote by f(R) the set of all evaluations of f(x
1, …, xn) on R. If F and G are generalized derivations of R such that [[F(x), x], [G(y), y]] ∈ Z(R) for any x, y ∈ f(R), then one of the following holds:
(1) |
there exists α ∈ C such that F(x) = αx for all x ∈ R 相似文献
8.
Yaochen Zhu 《数学学报(英文版)》2000,16(3):395-398
Let f (x) be a continued fraction with elements a
n
x, where coefficients a
n
are positive algebraic numbers. Using the criterion of [l] for any nonzero real algebraic numbers α1,...,αs with distinct absolute values the algebraic independence of the values f(α1), ..., f(αs) is proved under certain assumption concerning only with a
n
. For some transcendental numbers ξ the algebraic independence of values f(ξj)(j∈ℤ) is also established.
Received March 27, 1998, Accepted September 28, 1998 相似文献
9.
George F. Seelinger 《代数通讯》2013,41(1):237-248
10.
The additive subgroup generated by a polynomial 总被引:3,自引:0,他引:3
C. -L. Chuang 《Israel Journal of Mathematics》1987,59(1):98-106
SupposeR is a prime ring with the centerZ and the extended centroidC. Letp(x
1, …,x
n) be a polynomial overC in noncommuting variablesx
1, …,x
n. LetI be a nonzero ideal ofR andA be the additive subgroup ofRC generated by {p(a
1, …,a
n):a
1, …,a
n ∈I}. Then eitherp(x
1, …,x
n) is central valued orA contains a noncentral Lie ideal ofR except in the only one case whereR is the ring of all 2 × 2 matrices over GF(2), the integers mod 2. 相似文献
11.
Abstract. In 1950 Bang proposed a conjecture which became known as ``the plank conjecture': Suppose that a convex set S contained in the unit cube of R
n
and touching all its sides is covered by planks. (A plank is a set of the form {(x
1
, ..., x
n
): x
j
∈ I} for some j ∈ {1, ...,n} and a measurable subset I of [0, 1]. Its width is defined as |I| .) Then the sum of the widths of the planks is at least 1 . We consider a version of the conjecture in which the planks are fractional. Namely, we look at n -tuples f
1
, ..., f
n
of nonnegative-valued measurable functions on [0,1] which cover the set S in the sense that ∑ f
j
(x
j
) ≥ 1 for all (x
1
, ..., x
n
)∈ S . The width of a function f
j
is defined as ∈t
0
1
f
j
(x) dx . In particular, we are interested in conditions on a convex subset of the unit cube in R
n
which ensure that it cannot be covered by fractional planks (functions) whose sum of widths (integrals) is less than 1 . We prove that this (and, a fortiori, the plank conjecture) is true for sets which touch all edges incident with two antipodal
points in the cube. For general convex bodies inscribed in the unit cube in R
n
we prove that the sum of widths must be at least 1/n (the true bound is conjectured to be 2/n ). 相似文献
12.
Let R be a prime ring of characteristic different from 2, with Utumi quotient ring U and extended centroid C, δ a nonzero derivation of R, G a nonzero generalized derivation of R, and f(x 1, …, x n ) a noncentral multilinear polynomial over C. If δ(G(f(r 1, …, r n ))f(r 1, …, r n )) = 0 for all r 1, …, r n ∈ R, then f(x 1, …, x n )2 is central-valued on R. Moreover there exists a ∈ U such that G(x) = ax for all x ∈ R and δ is an inner derivation of R such that δ(a) = 0. 相似文献
13.
We study the problem of existence of periodic and almost periodic solutions of the scalar equation x′ (t) = − δx(t) + pmax
u∈[t − h, t]
x(u) + f(t) where δ, p ∈ R, with a periodic (almost periodic) perturbation f(t). For these solutions, we establish conditions of global exponential stability and prove uniqueness theorems.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 6, pp. 747–754, June, 1998. 相似文献
14.
Let Δ3 be the set of functions three times continuously differentiable on [−1, 1] and such that f″′(x) ≥ 0, x ∈ [−1, 1]. We prove that, for any n ∈ ℕ and r ≥ 5, there exists a function f ∈ C
r
[−1, 1] ⋂ Δ3 [−1, 1] such that ∥f
(r)∥
C[−1, 1] ≤ 1 and, for an arbitrary algebraic polynomial P ∈ Δ3 [−1, 1], there exists x such that
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