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1.
Vincenzo De Filippis 《Proceedings Mathematical Sciences》2010,120(3):285-297
Let R be a prime ring, U the Utumi quotient ring of R, C = Z(U) the extended centroid of R, L a non-central Lie ideal of R, H and G non-zero generalized derivations of R. Suppose that there exists an integer n ≥ 1 such that (H(u)u − uG(u))
n
= 0, for all u ∈ L, then one of the following holds: (1) there exists c ∈ U such that H(x) = xc, G(x) = cx; (2) R satisfies the standard identity s
4 and char (R) = 2; (3) R satisfies s
4 and there exist a, b, c ∈ U, such that H(x) = ax+xc, G(x) = cx+xb and (a − b)
n
= 0. 相似文献
2.
E. I. Bunina 《Journal of Mathematical Sciences》2008,152(2):155-190
It is proved that (elementary) Chevalley groups G
π(Φ,K) and G
π′(Φ′,K′) (or E
π(Φ,K) and E
π′(Φ′,K′)) over infinite fields K and K′ of characteristic different from 2, with weight lattices Λ and Λ′, respectively, are elementarily equivalent if and only
if the root systems Φ and Φ′ are isomorphic, the fields K and K′ are elementarily equivalent, and the lattices Λ and Λ′ coincide.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 8, pp. 29–77, 2006. 相似文献
3.
The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL
m
⊗GL
n
is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A
2 ≤ B ≤ A and nA,A
2 ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N
G
(E(m,n,R, A,B,C)). Bibliography: 46 titles. 相似文献
4.
Raffaele Mosca 《Graphs and Combinatorics》2001,17(3):517-528
Let G be a graph with n vertices, and denote as γ(G) (as θ(G)) the cardinality of a minimum edge cover (of a minimum clique cover) of G. Let E (let C) be the edge-vertex (the clique-vertex) incidence matrix of G; write then P(E)={x∈ℜ
n
:Ex≤1,x≥0}, P(C)={x∈ℜ
n
:Cx≤1,x≥0}, α
E
(G)=max{1
T
x subject to x∈P(E)}, and α
C
(G)= max{1
T
x subject to x∈P(C)}. In this paper we prove that if α
E
(G)=α
C
(G), then γ(G)=θ(G).
Received: May 20, 1998?Final version received: April 12, 1999 相似文献
5.
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
6.
Bertram Kostant 《Transformation Groups》2010,15(4):909-919
A proof (by Serre and by Cohen, Griess and Lisser) verified, in the special case of E
8, a conjecture of mine, that the finite projective group L
2(61) embeds in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . Subsequently, Griess and Ryba have shown (using computers) that L
2(49) and, in addition, (established by Serre without computers) L
2(41) also embed in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . That is, if K = 30, 24, 20 and k ∈ K then L
2(2k + 1) embeds in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) . In this paper we show that the “Borel” subgroup B(k) of L
2(2k + 1), k ∈ K, has a uniform construction. The theorem uses a result of T. Springer on the existence in
E8( \mathbbC ) {E_8}\left( \mathbb{C} \right) of three regular elements of the Weyl group, having orders k ∈ K, and associated to the regular, subregular and subsubregular nilpotent elements. Springer’s result generalizes (in the E
8 case) a 1959 general result of mine relating the principal nilpotent element with the Coxeter element. 相似文献
7.
Huanyin Chen 《Czechoslovak Mathematical Journal》2007,57(2):579-590
We characterize exchange rings having stable range one. An exchange ring R has stable range one if and only if for any regular a ∈ R, there exist an e ∈ E(R) and a u ∈ U(R) such that a = e + u and aR ⋂ eR = 0 if and only if for any regular a ∈ R, there exist e ∈ r.ann(a
+) and u ∈ U(R) such that a = e + u if and only if for any a, b ∈ R, R/aR ≅ R/bR ⇒ aR ≅ bR. 相似文献
8.
The paper deals with the structure of intermediate subgroups of the general linear group GL(n, k) of degree n over a field k of odd characteristic that contain a nonsplit maximal torus related to a radical extension of degree n of the ground field k. The structure of ideal nets over a ring that determine the structure of intermediate subgroups containinga transvection
is given. Let K = k( n?{d} ) K = k\left( {\sqrt[n]{d}} \right) be a radical degree-n extension of a field k of odd characteristic, and let T =(d) be a nonsplit maximal torus, which is the image of the multiplicative group of the field K under the regular embedding in G =GL(n, k). In the paper, the structure of intermediate subgroups H, T ≤ H ≤ G, that contain a transvection is studied. The elements of the matrices in the torus T = T (d) generate a subring R(d) in the field k.Let R be an intermediate subring, R(d) ⊆ R ⊆ k, d ∈ R. Let σR denote the net in which the ideal dR stands on the principal diagonal and above it and all entries of which beneath the principal diagonal are equal to R. Let σR denote the net in which all positions on the principal diagonal and beneath it are occupied by R and all entries above the principal diagonal are equal to dR. Let E(σR) be the subgroup generated by all transvections from the net group G(σR). In the paper it is proved that the product TE(σR) is a group (and thus an intermediate subgroup). If the net σ associated with an intermediate subgroup H coincides with σR,then TE(σR) ≤ H ≤ N(σR),where N(σR) is the normalizer of the elementary net group E(σR) in G. For the normalizer N(σR),the formula N(σR)= TG(σR) holds. In particular, this result enables one to describe the maximal intermediate subgroups. Bibliography: 13 titles. 相似文献
9.
Ji-pu Ma Tseng Yaun Rong Functional Analysis Research Center Harbin Normal University Harbin China 《中国科学A辑(英文版)》2007,50(9):1233-1239
Let E, F be two Banach spaces, and B(E, F), Φ(E, F), SΦ(E, F) and R(E,F) be the bounded linear, Fredholm, semi-Frdholm and finite rank operators from E into F, respectively. In this paper, using the continuity characteristics of generalized inverses of operators under small perturbations, we prove the following result Let ∑ be any one of the following sets {T ∈ Φ(E, F) IndexT =const, and dim N(T) = const.}, {T ∈ SΦ(E, F) either dim N(T) = const. < ∞ or codim R(T) = const.< ∞} and {T ∈ R(E, F) RankT =const.<∞}. Then ∑ is a smooth submanifold of B(E, F) with the tangent space TA∑ = {B ∈ B(E,F) BN(A) (∪) R(A)} for any A ∈ ∑. The result is available for the further application to Thom's famous results on the transversility and the study of the infinite dimensional geometry. 相似文献
10.
Let R be a prime ring with char R ≠ 2, L a non-central Lie ideal of R, d, g non-zero derivations of R, n ≥ 1 a fixed integer. We prove that if (d(x)x − xg(x))
n
= 0 for all x ∈ L, then either d = g = 0 or R satisfies the standard identity s
4 and d, g are inner derivations, induced respectively by the elements a and b such that a + b ∈ Z(R). 相似文献
11.
BASUDEB DHARA 《Proceedings Mathematical Sciences》2012,122(1):121-128
Let R be a prime ring with its Utumi ring of quotient U, H and G be two generalized derivations of R and L a noncentral Lie ideal of R. Suppose that there exists 0 ≠ a ∈ R such that a(H(u)u − uG(u))
n
= 0 for all u ∈ L, where n ≥ 1 is a fixed integer. Then there exist b′,c′ ∈ U such that H(x) = b′x + xc′, G(x) = c′x for all x ∈ R with ab′ = 0, unless R satisfies s
4, the standard identity in four variables. 相似文献
12.
Jie-Cheng Chen 《Israel Journal of Mathematics》1993,81(1-2):193-202
In this paper, we get a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n, v(x)dx) to weak-L
Φ(R
+
n+1
,dμ), where Φ is anN-function satisfying the Δ2-condition. We also find a necessary and sufficient condition on the weights (μ,v) for the Poisson integral operator to be bounded fromL
Φ(R
n,v(x)dx) toL
Φ(R
+
n+1
,dμ) under some additional condition.
Partially supported by NNSF of P.R. China 相似文献
13.
M. Zippin 《Israel Journal of Mathematics》1981,39(4):349-358
It is proved that there exists a positive function Φ(∈) defined for sufficiently small ∈ 〉 0 and satisfying limt→0 Φ(∈) =0 such that for any integersn 〉>0, ifQ is a projection ofl
1
n
onto ak-dimensional subspaceE with ‖|Q‖|≦1+∈ then there is an integerh〉=k(1−Φ(∈)) and anh-dimensional subspaceF ofE withd(F,l
1
h
) 〈= 1+Φ (∈) whered(X, Y) denotes the Banach-Mazur distance between the Banach spacesX andY. Moreover, there is a projectionP ofl
1
n
ontoF with ‖|P‖| ≦1+Φ(∈).
Author was partially supported by the N.S.F. Grant MCS 79-03042. 相似文献
14.
M. Abad J. P. Díaz Varela B. F. López Martinolich M. del C. Vannicola M. Zander 《Central European Journal of Mathematics》2006,4(4):547-561
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L
p,k, and the finite field F(p
k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L
p,k) generated by L
p,k into the variety V(F(p
k)) generated by F(p
k) and an interpretation Φ2 of V(F(p
k)) into V(L
p,k) such that Φ2Φ1(B) = B for every B ε V(L
p,k) and Φ1Φ2(R) = R for every R ε V(F(p
k)). 相似文献
15.
Let L(H) denote the algebra of all bounded linear operators on a separable infinite dimensional complex Hilbert space H into itself. Given A ∈ L(H), we define the elementary operator Δ
A
: L(H) → L(H) by Δ
A
(X) = AXA − X. In this paper we study the class of operators A ∈ L(H) which have the following property: ATA = T implies AT*A = T* for all trace class operators T ∈ C
1(H). Such operators are termed generalized quasi-adjoints. The main result is the equivalence between this character and the
fact that the ultraweak closure of the range of Δ
A
is closed under taking adjoints. We give a characterization and some basic results concerning generalized quasi-adjoints
operators. 相似文献
16.
Abraham Neyman 《Israel Journal of Mathematics》1984,48(2-3):129-138
For fixed 1≦p<∞ theL
p-semi-norms onR
n
are identified with positive linear functionals on the closed linear subspace ofC(R
n
) spanned by the functions |<ξ, ·>|
p
, ξ∈R
n
. For every positive linear functional σ, on that space, the function Φσ:R
n
→R given by Φσ is anL
p-semi-norm and the mapping σ→Φσ is 1-1 and onto. The closed linear span of |<ξ, ·>|
p
, ξ∈R
n
is the space of all even continuous functions that are homogeneous of degreep, ifp is not an even integer and is the space of all homogeneous polynomials of degreep whenp is an even integer. This representation is used to prove that there is no finite list of norm inequalities that characterizes
linear isometric embeddability, in anyL
p unlessp=2.
Supported by the National Science Foundation MCS-79-06634 at U.C. Berkeley. 相似文献
17.
It is well known that in the case of the Luxemburg normE
Φ (resp.h
Φ) is anM ideal inL
Φ (resp.l
Φ), see [1], [9], [15] and [6]; [17] and [18]. It is proved in this paper that in the case of the Orlicz normE
Φ (resph
Φ) is anM-ideal inL
Φ (resp.l
Φ) iff Φ satisfies the suitable Δ2 or Φ*(a(Φ*)), where a(Φ*) is linear on the interval [0,u]} and Φ* denotes the function complementary to Φ in the sense of Young. It is also proved that any linear continuous regular (i.e.
order continuous) functional ξυ overE
Φ (resp.h
Φ) generated byv∈ L(h
Φ*) (resp.v∈ L(h
Φ*)) which attains its norm on the unit sphereS(E
Φ) (resp.S(h
Φ)), has a unique norm-preserving extension toL
Φ (resp.l
Φ). Finally, it is proved thatL
Φ (resp.l
Φ) has the property that any linear continuous regular functional ξυ overE
Φ (resp.h
Φ) has a unique norm-preserving extension toL
Φ (resp.l
Φ) iff Φ orE
Φ satisfies the suitable Δ2 and in the second case Φ* attains the value 1. 相似文献
18.
Thierry De Pauw 《Journal of Geometric Analysis》2002,12(1):29-61
A concentrated (ξ, m) almost monotone measure inR
n
is a Radon measure Φ satisfying the two following conditions: (1) Θ
m
(Φ,x)≥1 for every x ∈spt (Φ) and (2) for everyx ∈R
n
the ratioexp [ξ(r)]r−mΦ(B(x,r)) is increasing as a function of r>0. Here ξ is an increasing function such thatlim
r→0-ξ(r)=0. We prove that there is a relatively open dense setReg (Φ) ∋spt (Φ) such that at each x∈Reg(Φ) the support of Φ has the following regularity property: given ε>0 and λ>0 there is an m dimensional spaceW ⊂R
n
and a λ-Lipschitz function f from x+W into x+W‖ so that (100-ε)% ofspt(Φ) ∩B (x, r) coincides with the graph of f, at some scale r>0 depending on x, ε, and λ. 相似文献
19.
Pavel Shumyatsky 《Israel Journal of Mathematics》1994,87(1-3):111-116
Letp be a prime,G a periodic solvablep′-group acted on by an elementary groupV of orderp
2. We show that ifC
G(v) is abelian for eachv ∈V
# thenG has nilpotent derived group, and ifp=2 andC
G(v) is nilpotent for eachv ∈V
# thenG is metanilpotent. Earlier results of this kind were known only for finite groups. 相似文献
20.
Let (G, χ, x) be a triple consisting of a finitely presented groupG, epimorphism χ:G →Z, and distinguished elementx ∈G such that χ(x)=1. Given a finite symmetric groupS
r, we construct a finite directed graph Γ that describes the set Φ
r
of representations π: Ker χ →S
r as well as the mapping σ
x
:Φ
r
→Φ
r
defined by (σ
x
ϱ)(a) = ϱ(x
−1
ax) for alla ∈ Ker χ. The pair (Φ
r
,σ
x
has the structure of a shift of finite type, a well-known type of compact 0-dimensional dynamical system. We discuss basic
properties and applications of therepresentation shift (Φ
r
,σ
x
), including applications to knot theory. 相似文献
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