共查询到20条相似文献,搜索用时 31 毫秒
1.
Gabriel Navarro Pham Huu Tiep 《Proceedings of the American Mathematical Society》2006,134(10):2833-2837
If is a prime number and is a finite group, we show that has an irreducible complex character of degree not divisible by with values in the cyclotomic field .
2.
I. M. Isaacs Thomas Michael Keller U. Meierfrankenfeld Alexander Moretó 《Proceedings of the American Mathematical Society》2006,134(11):3123-3130
Let be a finite group that acts on a nonzero finite dimensional vector space over an arbitrary field. Assume that is completely reducible as a -module, and that fixes no nonzero vector of . We show that some element has a small fixed-point space in . Specifically, we prove that we can choose so that , where is the smallest prime divisor of .
3.
Kamran Divaani-Aazar Mohammad Ali Esmkhani Massoud Tousi 《Proceedings of the American Mathematical Society》2006,134(10):2817-2822
Let be a commutative ring with identity and an -module. It is shown that if is pure injective, then is isomorphic to a direct summand of the direct product of a family of finitely embedded modules. As a result, it follows that if is Noetherian, then is pure injective if and only if is isomorphic to a direct summand of the direct product of a family of Artinian modules. Moreover, it is proved that is pure injective if and only if there is a family of -algebras which are finitely presented as -modules, such that is isomorphic to a direct summand of a module of the form , where for each , is an injective -module.
4.
Shoyu Nagaoka 《Proceedings of the American Mathematical Society》2006,134(9):2533-2540
In this paper we generalize the notion of -adic modular form to the Hermitian modular case and prove a formula that shows a coincidence between certain -adic Hermitian Eisenstein series and the genus theta series associated with Hermitian matrix with determinant .
5.
Madjid Mirzavaziri Mohammad Sal Moslehian 《Proceedings of the American Mathematical Society》2006,134(11):3319-3327
Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed.
6.
Desmond Sheiham 《Proceedings of the American Mathematical Society》2006,134(12):3465-3474
If is a triangular matrix ring, the columns and are f.g. projective -modules. We describe the universal localization of which makes invertible an -module morphism , generalizing a theorem of A. Schofield. We also describe the universal localization of -modules.
7.
Nafaa Chbili 《Proceedings of the American Mathematical Society》2008,136(6):2217-2224
Przytycki and Sokolov proved that a three-manifold admits a semi-free action of the finite cyclic group of order with a circle as the set of fixed points if and only if is obtained from the three-sphere by surgery along a strongly -periodic link . Moreover, if the quotient three-manifold is an integral homology sphere, then we may assume that is orbitally separated. This paper studies the behavior of the coefficients of the Conway polynomial of such a link. Namely, we prove that if is a strongly -periodic orbitally separated link and is an odd prime, then the coefficient is congruent to zero modulo for all such that .
8.
Esther Beneish 《Proceedings of the American Mathematical Society》2006,134(7):1869-1873
Let be a prime greater than , and let be the semi-direct product of a group of order by a cyclic group of order , which acts faithfully on . Let be the localization of at . We show that the Krull-Schmidt Theorem fails for the category of invertible -lattices.
9.
Yuming Liu 《Proceedings of the American Mathematical Society》2006,134(6):1605-1613
Let and be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence between and such that is induced by exact functors. We present a nice correspondence between indecomposable modules over and . As a consequence, we have the following: (1) If is a self-injective algebra, then so is ; (2) If and are finite dimensional algebras over an algebraically closed field , and if is of finite representation type such that the Auslander-Reiten quiver of has no oriented cycles, then and are Morita equivalent.
10.
David H. Bailey Michal Misiurewicz 《Proceedings of the American Mathematical Society》2006,134(9):2495-2501
A real number is said to be -normal if every -long string of digits appears in the base- expansion of with limiting frequency . We prove that is -normal if and only if it possesses no base- ``hot spot'. In other words, is -normal if and only if there is no real number such that smaller and smaller neighborhoods of are visited by the successive shifts of the base- expansion of with larger and larger frequencies, relative to the lengths of these neighborhoods.
11.
Phil Hanlon 《Proceedings of the American Mathematical Society》2006,134(7):1857-1867
Let be a poset with unique minimal and maximal elements and . For each , let be the vector space spanned by -chains from to in . We define the notion of a Hodge structure on which consists of a local action of on , for each , such that the boundary map intertwines the actions of and according to a certain condition.
We show that if has a Hodge structure, then the families of Eulerian idempotents intertwine the boundary map, and so we get a splitting of into Hodge pieces.
We consider the case where is , the poset of subsets of with cardinality divisible by is fixed, and is a multiple of . We prove a remarkable formula which relates the characters of acting on the Hodge pieces of the homologies of the to the characters of acting on the homologies of the posets of partitions with every block size divisible by .
12.
Paul Binding Lyonell Boulton Jan Cepicka Pavel Drá bek Petr Girg 《Proceedings of the American Mathematical Society》2006,134(12):3487-3494
For , the eigenfunctions of the non-linear eigenvalue problem for the -Laplacian on the interval are shown to form a Riesz basis of and a Schauder basis of whenever .
13.
Let be a simplex and a compact subset of the set of all extreme points of . We show that any bounded function of Baire class on can be extended to a function of affine class on . Moreover, can be chosen in such a way that .
14.
Roberto Camporesi 《Proceedings of the American Mathematical Society》2006,134(9):2649-2659
We prove the Paley-Wiener theorem for the spherical transform on the complex Grassmann manifolds SUSU U. This theorem characterizes the -biinvariant smooth functions on the group that are supported in the -invariant ball of radius , with less than the injectivity radius of , in terms of holomorphic extendability, exponential growth, and Weyl invariance properties of the spherical Fourier transforms , originally defined on the discrete set of highest restricted spherical weights.
15.
Given a decreasing weight and an Orlicz function satisfying the -condition at zero, we show that the Orlicz-Lorentz sequence space contains an -isomorphic copy of , if and only if the Orlicz sequence space does, that is, if , where and are the Matuszewska-Orlicz lower and upper indices of , respectively. If does not satisfy the -condition, then a similar result holds true for order continuous subspaces and of and , respectively.
16.
Amir Akbary 《Proceedings of the American Mathematical Society》2006,134(11):3143-3151
Let be a newform of even weight , level and character and let be a newform of even weight , level and character . We give a generalization of a theorem of Elliott, regarding the average values of Dirichlet -functions, in the context of twisted modular -functions associated to and . Using this result, we find a lower bound in terms of for the number of primitive Dirichlet characters modulo prime whose twisted product -functions are non-vanishing at a fixed point with .
17.
Bo-Hae Im 《Proceedings of the American Mathematical Society》2006,134(6):1623-1630
Let be a number field, an algebraic closure of , the absolute Galois group , the maximal abelian extension of and an elliptic curve defined over . In this paper, we prove that if all 2-torsion points of are -rational, then for each , has infinite rank, and hence has infinite rank.
18.
Given a perfect field of characteristic , a smooth proper -scheme , a crystal on relative to and a finite group acting on and , we show that, viewed as a virtual -module, the reduction modulo of the crystalline cohomology of is the de Rham cohomology of modulo . On the way we prove a base change theorem for the virtual -representations associated with -equivariant objects in the derived category of -modules.
19.
Tzu-Chun Lin 《Proceedings of the American Mathematical Society》2006,134(6):1599-1604
Let be a faithful representation of a finite group over the field . Via the group acts on and hence on the algebra of homogenous polynomial functions on the vector space . R. Kane (1994) formulated the following result based on the work of R. Steinberg (1964): If the field has characteristic 0, then is a Poincaré duality algebra if and only if is a pseudoreflection group. The purpose of this note is to extend this result to the case (i.e. the order of is relatively prime to the characteristic of ).
20.
Andrei S. Rapinchuk Louis Rowen Yoav Segev 《Proceedings of the American Mathematical Society》2006,134(11):3107-3114
Given a quaternion division algebra a noncentral element is called pure if its square belongs to the center. A theorem of Rowen and Segev (2004) asserts that for any quaternion division algebra of positive characteristic and any pure element the quotient of by the normal subgroup generated by is abelian-by-nilpotent-by-abelian. In this note we construct a quaternion division algebra of characteristic zero containing a pure element such that contains a nonabelian free group. This demonstrates that the situation in characteristic zero is very different.