共查询到20条相似文献,搜索用时 31 毫秒
1.
Siman Wong 《manuscripta mathematica》2000,102(1):129-137
Given a prime l and an elliptic curve E defined over a number field k, we show that a non-zero point P] E(k) lies in lE(k) if and only if P lies in lE(k)(mod ) for almost all finite primes of k. We give conditions on l under which analogous results hold for Abelian varieties and with one point replaced by a finite number of points. We also construct examples to show that these conditions are essential. 相似文献
2.
J. Murray 《Archiv der Mathematik》2001,77(5):373-377
Let G be a finite group and let F be a splitting field of characteristic $ p > 0 $ p > 0 . We show that I2 = E0, where I is a certain ideal of the centre Z of FG, and E0 is the span of the block idempotents of defect zero. 相似文献
3.
Kurt Leichtweiß 《Archiv der Mathematik》1999,72(4):315-320
Due to R. Schneider 1967 an ellipsoid E in the affine space
\Bbb An\Bbb A^n is affinely rigid, i.e. every other ovaloid F in
\Bbb An\Bbb A^n with the same affine Blaschke metric as for E equals E up to an equiaffine motion of E. Due to M. Kozlowski 1985 resp. W. Blaschke 1922 for n = 3 ellipsoids are moreover S-rigid resp. infinitesimally S-rigid in the sense of equal resp. infinitesimally equal affine scalar curvature S (unknown until now for n >3). - In this article it is proved that ellipsoids in
\Bbb An\Bbb A^n are also infinitesimally S-rigid for any n. 相似文献
4.
P. Longobardi 《Archiv der Mathematik》2001,76(2):88-90
A group G is said to be in Ek*E_k^* (k a positive integer), if every infinite subset of G contains a pair of elements that generate a k-Engel group.¶It is shown that a finitely generated locally graded group G in Ek*E_k^* is a finite-by- (k-Engel) group, in particular a finite extension of a k-Engel group. 相似文献
5.
The main aim of this paper is to obtain a dual result to the now well known Auslander-Bridger formula for G-dimension. We will show that if R is a complete Cohen-Macaulay ring with residue field k, and M is a non-injective h-divisible Ext-finite R-module of finite Gorenstein injective dimension such that for each i 3 1i \geq 1 Exti (E,M) = 0 for all indecomposable injective R-modules E 1 E(k)E \neq E(k), then the depth of the ring is equal to the sum of the Gorenstein injective dimension and Tor-depth of M. As a consequence, we get that this formula holds over a d-dimensional Gorenstein local ring for every nonzero cosyzygy of a finitely generated R-module and thus in particular each such nth cosyzygy has its Tor-depth equal to the depth of the ring whenever n 3 dn \geq d. 相似文献
6.
Alexander Schrijver 《Combinatorica》2000,20(4):575-588
Let G=(V, E, A) be a mixed graph. That is, (V, E) is an undirected graph and (V, A) is a directed graph. A matching forest (introduced by R. Giles) is a subset F of EèAE\cup A such that F contains no circuit (in the underlying undirected graph) and such that for each v ? Vv\in V there is at most one e ? Fe\in F such that v is head of e. (For an undirected edge e, both ends of e are called head of e.) Giles gave a polynomial-time algorithm to find a maximum-weight matching forest, yielding as a by-product a characterization of the inequalities determining the convex hull of the incidence vectors of the matching forests. We prove that these inequalities form a totally dual integral system. It is equivalent to an ``all-integer' min-max relation for the maximum weight of a matching forest. Our proof is based on an exchange property for matching forests, and implies Giles' characterization. 相似文献
7.
Within the class of regular E-solid semigroups, a theory of e-varieties including appropriate notions of biidentities and biinvariant congruences is presented, such that, together with bifree objects, these notions inherit the properties and interrelations well known from universial algebra. This theory generalizes the previously developed such theory for orthodox semigroups. As an application, the bifree objects in certain e-varieties of E-solid locally orthodox semigroups, which are constructed by means of Malcev products from a varities of bands, groups and completely simple semigroups, are described as subsemigroups in suitable Pastijn products of some bands by relatively bifree completely simple semigroups. As a consequence, it follows that every regular E-solid locally orthodox semigroup regularly divides a so-called solid Pastijn product of a band by a completely simple semigroup. 相似文献
8.
M. Wójtowicz 《Archiv der Mathematik》2000,75(5):376-379
We present a relatively short proof of the following generalization of a theorem due to Lozanovskii, Mekler and Meyer-Nieberg: A s\sigma -Dedekind complete locally convex-solid Riesz space E contains no copy of l¥l_{\infty } iff E contains no lattice copy of l¥l_{\infty } (Theorem and Corollary 1). 相似文献
9.
Let {(Xi,|| · || i)}i ? I,\{(X_i,\left \| {\cdot } \right \| _{i})\}_{i\in I}, be an arbitrary family of normed spaces and let (E,|| · || E)(E,\left \| {\cdot } \right \| _{E}) be a monotonic normed space of real functions on the set I that is an ideal in \Bbb RI{\Bbb R}^I. We prove a sufficient condition for the direct sum space E(Xi) to be uniformly rotund in a direction. We show that this condition is also necessary for E=l¥E=\ell _{\infty }, and it is not necessary for E=l1E=\ell _1. When E is either uniformly rotund in every direction and has compact order intervals, or weakly uniformly rotund respect to its evaluation functionals, we reestablish as a corollary the result that reads: E(Xi)E(X_i) is uniformly rotund in every direction if and only if so are all the Xi. 相似文献
10.
Group Connectivity of 3-Edge-Connected Chordal Graphs 总被引:3,自引:0,他引:3
Hong-Jian Lai 《Graphs and Combinatorics》2000,16(2):165-176
Let A be a finite abelian group and G be a digraph. The boundary of a function f: E(G)ZA is a function f: V(G)ZA given by f(v)=~e leaving vf(e)m~e entering vf(e). The graph G is A-connected if for every b: V(G)ZA with ~v] V(G) b(v)=0, there is a function f: E(G)ZA{0} such that f=b. In [J. Combinatorial Theory, Ser. B 56 (1992) 165-182], Jaeger et al showed that every 3-edge-connected graph is A-connected, for every abelian group A with |A|̈́. It is conjectured that every 3-edge-connected graph is A-connected, for every abelian group A with |A|̓ and that every 5-edge-connected graph is A-connected, for every abelian group A with |A|́.¶ In this note, we investigate the group connectivity of 3-edge-connected chordal graphs and characterize 3-edge-connected chordal graphs that are A-connected for every finite abelian group A with |A|́. 相似文献
11.
J.-F. Bony 《Annales Henri Poincare》2002,3(4):693-710
Résumé. On travaille dans le cadre de lanalyse semi-classique. Considérons p(x, hDx) p(x, hD_{x}) , une perturbation de -h2D -h^{2}\Delta qui est analytique à linfini. On suppose que dans la surface dénergie E0 > 0, les points critiques du symbole p(x, x) p(x, \xi) forment une sous-variété C \mathcal C et que p est non dégénéré dans lespace normal à C \mathcal C .¶En utilisant les résultats de [6] et [18], on obtient une majoration du nombre de résonances dans des disques de rayon d \delta centrés en E proche de E0, où d \delta satisfait Ch < d \delta < 1/C pour une constante C > 0. En généralisant la formule de trace de Sjöstrand qui exprime la trace dune différence dopérateurs en fonction des résonances, on trouve une minoration du nombre de résonances proches de E0. 相似文献
12.
The Euler monoid En = {(a,b,t) epsilon Z3 : a2 + b2 = tn, n S 1, is free if and only if n is odd (Theorem 1). We extend the results of Lyndon and Ullman, and Beardon concerning the set of those rational numbers mu epsilon (-2,2) for which the matrix Möbius group Gmu generated by A= and B = is not free (Theorems 2, 3, 4). 相似文献
13.
S. Kawata 《Archiv der Mathematik》2000,75(2):92-97
Let G be a finite group and O{\cal O} a complete discrete valuation ring of characteristic zero with maximal ideal (p)(\pi ) and residue field k = O/(p)k = {\cal O}/(\pi ) of characteristic p > 0. Let S be a simple kG-module and QS a projective O G{\cal O} G-lattice such that QS / pQSQ_S / \pi Q_S is a projective cover of S. We show that if S is liftable and QS belongs to a block of O G{\cal O} G of infinite representation type, then the standard Auslander-Reiten sequence terminating in W-1S\Omega ^{-1}S is a direct summand of the short exact sequence obtained from some Auslander-Reiten sequence of OG{\cal O}G-lattices by reducing each term mod (p)(\pi ). 相似文献
14.
Y. Choi 《Archiv der Mathematik》2001,77(3):222-232
We study the mod 2 homology of the double loop space of SU(n)/SO(n) using the Serre spectral sequence along with the Eilenberg-Moore spectral sequence. Then we also get the homology of the double loop space of the set of all Lagrangian subspaces of the symplectic vector space R2n. 相似文献
15.
The algebra Bp(\Bbb R){\cal B}_p({\Bbb R}), p ? (1,¥)\{2}p\in (1,\infty )\setminus \{2\}, consisting of all measurable sets in \Bbb R{\Bbb R} whose characteristic function is a Fourier p-multiplier, forms an algebra of sets containing many interesting and non-trivial elements (e.g. all intervals and their finite unions, certain periodic sets, arbitrary countable unions of dyadic intervals, etc.). However, Bp(\Bbb R){\cal B}_p({\Bbb R}) fails to be a s\sigma -algebra. It has been shown by V. Lebedev and A. Olevskii [4] that if E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}), then E must coincide a.e. with an open set, a remarkable topological constraint on E. In this note we show if $2 < p < \infty $2 < p < \infty , then there exists E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}) which is not in Bq(\Bbb R){\cal B}_q({\Bbb R}) for any q > pq>p. 相似文献
16.
Andrea Lucchini 《Archiv der Mathematik》1999,73(4):241-248
For any fixed k 3 7k \geq 7 there exist integers nk and ak such that if the ring R is generated by a set of m elements t1,...,tm, where 2t1-t122t_1-t_1^2 is a unit of finite multiplicative order, and n 3 nk+makn \geq n_k+ma_k, then the group En(R) generated by elementary transvections is an epimorphic image of the triangle group D(2,3,k).\Delta (2,3,k). 相似文献
17.
Lajos Rónyai 《Combinatorica》2000,20(4):569-573
A classic theorem of Erdis, Ginzburg and Ziv states that in a sequence of 2n-1 integers there is a subsequence of length n whose sum is divisble by n. This result has led to several extensions and generalizations. A multi-dimensional problem from this line of research is the following. Let ZnZ_n stand for the additive group of integers modulo n. Let s(n, d) denote the smallest integer s such that in any sequence of s elements from ZndZ_n^d (the direct sum of d copies of ZnZ_n) there is a subsequence of length n whose sum is 0 in ZndZ_n^d. Kemnitz conjectured that s(n, 2) = 4n - 3. In this note we prove that s(p,2) £ 4p - 2s(p,2) \le 4p - 2 holds for every prime p. This implies that the value of s(p, 2) is either 4p-3 or 4p-2. For an arbitrary positive integer n it follows that s(n, 2) £ (41/10)ns(n, 2) \le (41/10)n. The proof uses an algebraic approach. 相似文献
18.
The pebbling number of a graph G, f(G), is the least m such that, however m pebbles are placed on the vertices of G, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and placing one on an adjacent vertex. It is conjectured that for all graphs G and H, f(G 2H)hf(G)f(H).¶Let Cm and Cn be cycles. We prove that f(Cm 2Cn)hf(Cm) f(Cn) for all but a finite number of possible cases. We also prove that f(G2T)hf(G) f(T) when G has the 2-pebbling property and T is any tree. 相似文献
19.
Conchita Martínez-Pérez 《Archiv der Mathematik》2003,80(1):25-36
The subject of this paper is the relationship between the set of chief factors of a finite group G and extensions of an irreducible
\mathbbK \mathbb{K} G-module U (
\mathbbK \mathbb{K} a field). Let H / L be a p-chief factor of G. We prove that, if H / L is complemented in a vertex of U, then there is a short exact sequence of Ext-functors for the module U and any
\mathbbK \mathbb{K} G-module V. In some special cases, we prove the converse, which is false in general. We also consider the intersection of the centralizers of all the extensions of U by an irreducible module and provide new bounds for this group. 相似文献
20.
For a given number field K and any prime l\ell we construct an increasing sequence of l\ell -extensions Kn of K which are locally cyclotomic over K. We give various criterious of finiteness or non-finiteness of this l\ell -tower and we characterise the number fields which have such a finite tower in terms of Iwasawa theory. 相似文献