共查询到20条相似文献,搜索用时 156 毫秒
1.
Masaharu Kusuda 《Proceedings of the American Mathematical Society》2003,131(10):3075-3081
Let be a -algebra and let be a full (right) Hilbert -module. It is shown that if the spectrum of is discrete, then every closed --submodule of is complemented in , and conversely that if is a -space and if every closed --submodule of is complemented in , then is discrete.
2.
Florian Enescu 《Proceedings of the American Mathematical Society》2003,131(11):3379-3386
The notion of stability of the highest local cohomology module with respect to the Frobenius functor originates in the work of R. Hartshorne and R. Speiser. R. Fedder and K.-i. Watanabe examined this concept for isolated singularities by relating it to -rationality. The purpose of this note is to study what happens in the case of non-isolated singularities and to show how this stability concept encapsulates a few of the subtleties of tight closure theory. Our study can be seen as a generalization of the work by Fedder and Watanabe. We introduce two new ring invariants, the -stability number and the set of -stable primes. We associate to every ideal generated by a system of parameters and an ideal of multipliers denoted and obtain a family of ideals . The set is independent of and consists of finitely many prime ideals. It also equals prime ideal such that is -stable. The maximal height of such primes defines the -stability number.
3.
Fernando Szechtman 《Proceedings of the American Mathematical Society》2003,131(12):3657-3664
We refer to an automorphism of a group as -inner if given any subset of with cardinality less than , there exists an inner automorphism of agreeing with on . Hence is 2-inner if it sends every element of to a conjugate. New examples are given of outer -inner automorphisms of finite groups for all natural numbers .
4.
Gabriel Navarro 《Proceedings of the American Mathematical Society》2003,131(10):3019-3020
If is a finite group and is a prime number, let be the number of Sylow -subgroups of . If is a subgroup of a -solvable group , we prove that divides .
5.
Michael J. Fisher 《Proceedings of the American Mathematical Society》2003,131(11):3617-3621
Let be a fixed odd prime. In this paper we prove an exponent conjecture of Bousfield, namely that the -exponent of the spectrum is for . It follows from this result that the -exponent of is at least for and , where denotes the -connected cover of .
6.
Fabio Nicola 《Proceedings of the American Mathematical Society》2003,131(9):2841-2848
We are concerned with the so-called -pseudo-differential calculus. We describe the spectrum of the unital and commutative -algebra given by the norm closure of the space of -order pseudo-differential operators modulo compact operators; other related algebras are also considered. Finally, their -theory is computed.
7.
Huaxin Lin 《Proceedings of the American Mathematical Society》2003,131(12):3813-3819
Let be a unital simple -algebra with real rank zero. It is shown that if satisfies a so-called fundamental comparison property, then has tracial topological rank zero. Combining some previous results, it is shown that a unital simple -algebra with real rank zero, stable rank one and weakly unperforated must have slow dimension growth.
8.
Hui Li 《Proceedings of the American Mathematical Society》2003,131(11):3579-3582
Let be a connected, compact symplectic manifold equipped with a Hamiltonian action. We prove that, as fundamental groups of topological spaces, , where is the symplectic quotient at any value in the image of the moment map .
9.
Lin Chen Ruan Yingbin Yan Zikun 《Proceedings of the American Mathematical Society》2003,131(9):2753-2759
We prove that if are injective, then is subscalar if and only if is subscalar. As corollaries, it is shown that -hyponormal operators and log-hyponormal operators are subscalar; also w-hyponormal operators with Ker Kerand their generalized Aluthge transformations are subscalar.
10.
Dong-Ho Tsai 《Proceedings of the American Mathematical Society》2003,131(10):3067-3074
We consider a special type of parabolic Monge-Ampère equation on arising from convex hypersurfaces expansion in Euclidean spaces. We obtained a parabolic estimate of the support functions for the convex hypersurfaces assuming that we have already had a parabolic estimate.
11.
Chandrashekhar Khare 《Proceedings of the American Mathematical Society》2003,131(10):3021-3023
In this note we relate the property of a semisimple -adic Galois representation being ``-split' to its having abelian image.
12.
Rajna Rajic 《Proceedings of the American Mathematical Society》2003,131(10):3043-3051
Let be a Hilbert -module over the -algebra of all compact operators on a complex Hilbert space . Given an orthogonal projection , we describe the set for an arbitrary adjointable operator . The relationship between the set and the matricial range of is established.
13.
Akira Kono James P. Lin Osamu Nishimura 《Proceedings of the American Mathematical Society》2003,131(10):3289-3295
It is shown that the mod 3 cohomology of a homotopy associative mod 3 -space which is rationally equivalent to the Lie group and which has integral 3-torsion is isomorphic to that of as a Hopf algebra over the mod 3 Steenrod algebra.
14.
Let be a rational prime and a positive rational integer coprime with . Denote by the number of solutions of the equation in rational integers and . In a paper of Le, he claimed that without giving a proof. Furthermore, the statement has been used by Le, Bugeaud and Shorey in their papers to derive results on certain Diophantine equations. In this paper we point out that the statement is incorrect by proving that .
15.
Flavio Abdenur Artur Avila Jairo Bochi 《Proceedings of the American Mathematical Society》2004,132(3):699-705
We prove that nontrivial homoclinic classes of -generic flows are topologically mixing. This implies that given , a nontrivial -robustly transitive set of a vector field , there is a -perturbation of such that the continuation of is a topologically mixing set for . In particular, robustly transitive flows become topologically mixing after -perturbations. These results generalize a theorem by Bowen on the basic sets of generic Axiom A flows. We also show that the set of flows whose nontrivial homoclinic classes are topologically mixing is not open and dense, in general.
16.
17.
Teresa Crespo 《Proceedings of the American Mathematical Society》2004,132(3):691-695
We present an explicit construction of the complete family of Galois extensions of a field of characteristic 3 with Galois group the central product of a double cover of the symmetric group and the quaternion group , containing a given -extension of the field .
18.
N. Bejhaj Rhouma 《Proceedings of the American Mathematical Society》2003,131(12):3747-3755
We show the existence of principal eigenvalues of the problem in where is an indefinite weight function. The existence of a continuous family of principal eigenvalues is demonstrated. Also, we prove the existence of a principal eigenvalue for which the principal eigenfunction at .
19.
Naotsugu Chinen 《Proceedings of the American Mathematical Society》2003,131(11):3547-3551
Let be a continuous map from the circle to itself. The main result of this paper is that the topological entropy of is positive if and only if has an infinite -limit set which contains a periodic orbit.
20.
Enrico Leuzinger 《Proceedings of the American Mathematical Society》2004,132(3):919-927
Let be a noncompact semisimple Lie group and an arbitrary discrete, torsion-free subgroup of . Let be the bottom of the spectrum of the Laplace-Beltrami operator on the locally symmetric space , and let be the exponent of growth of . If has rank , then these quantities are related by a well-known formula due to Elstrodt, Patterson, Sullivan and Corlette. In this note we generalize that relation to the higher rank case by estimating from above and below by quadratic polynomials in . As an application we prove a rigiditiy property of lattices.