共查询到20条相似文献,搜索用时 31 毫秒
1.
Vijay Kodiyalam 《Proceedings of the American Mathematical Society》2000,128(2):407-411
Let be a polynomial ring over a field. For a graded -module generated in degree at most , the Castelnuovo-Mumford regularity of each of (i) its symmetric power, (ii) its torsion-free symmetric power and (iii) the integral closure of its torsion-free symmetric power is bounded above by a linear function in with leading coefficient at most . For a graded ideal of , the regularity of is given by a linear function of for all sufficiently large . The leading coefficient of this function is identified.
2.
Alexandre Eremenko 《Proceedings of the American Mathematical Society》2000,128(2):557-560
Bloch's Theorem is extended to -quasiregular maps , where is the standard -dimensional sphere. An example shows that Bloch's constant actually depends on for .
3.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .
4.
Let be a prime number and let be the group of all invertible matrices over the prime field . It is known that every irreducible -module can occur as a submodule of , the polynomial algebra with variables over . Given an irreducible -module , the purpose of this paper is to find out the first value of the degree of which occurs as a submodule of , the subset of consisting of homogeneous polynomials of degree . This generalizes Schwartz-Tri's result to the case of any prime .
5.
Robert Myers 《Proceedings of the American Mathematical Society》2000,128(5):1563-1566
This paper gives a new proof of a result of Geoghegan and Mihalik which states that whenever a contractible open -manifold which is not homeomorphic to is a covering space of an -manifold and either or and is irreducible, then the group of covering translations injects into the homeotopy group of .
6.
Byeong-Kweon Oh 《Proceedings of the American Mathematical Society》2000,128(3):683-689
Let be the minimal rank of -universal -lattices, by which we mean positive definite -lattices which represent all positive -lattices of rank . It is a well known fact that for . In this paper, we determine and find all -universal lattices of rank for .
7.
Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2000,128(2):521-525
We show that the celebrated Lomonosov theorem cannot be improved by increasing the number of commuting operators. Specifically, we prove that if is the operator without a non-trivial closed invariant subspace constructed by C. J. Read, then there are three operators , and (non-multiples of the identity) such that commutes with , commutes with , commutes with , and is compact. It is also shown that the commutant of contains only series of .
8.
Michel Van den Bergh 《Proceedings of the American Mathematical Society》2000,128(2):375-381
Assume that is a surface over an algebraically closed field . Let be obtained from by blowing up a smooth point and let be the exceptional curve. Let be the category of coherent sheaves on . In this note we show how to recover from , if we know the object .
9.
Given a Banach space and an integer , the existence of an -homogeneous polynomial which is not uniformly continuous with respect to the polynomial topology on is investigated. We provide a complete characterization for some classical Banach spaces, while for others a surprising unresolved difficulty is encountered for a certain value of (depending on ).
10.
M. Beattie S. Dascalescu L. Grü nenfelder 《Proceedings of the American Mathematical Society》2000,128(2):361-367
In this note we describe nonsemisimple Hopf algebras of dimension with coradical isomorphic to , abelian of order , over an algebraically closed field of characteristic zero. If is cyclic or , then we also determine the number of isomorphism classes of such Hopf algebras.
11.
Yongkuk Kim 《Proceedings of the American Mathematical Society》2000,128(5):1497-1506
Codimension-2 fibrators are -manifolds which automatically induce approximate fibration, in the following sense: given any proper mapping from an -manifold onto a -manifold such that each point-preimage is a copy of the codimension-2 fibrator, is necessarily an approximate fibration. In this paper, we give some answers to the following question: given an -manifold which is a nontrivial connected sum, when is a codimension-2 fibrator?
12.
A generalization of Kwack's theorem to the infinite dimensional case is obtained. We consider a holomorphic map from into , where is a hypersurface in a complex Banach manifold and is a hyperbolic Banach space. Under various assumptions on , and we show that can be extended to a holomorphic map from into . Moreover, it is proved that an increasing union of pseudoconvex domains containing no complex lines has the Hartogs extension property.
13.
Paolo Lipparini 《Proceedings of the American Mathematical Society》2000,128(2):605-609
We prove the following: Theorem A. If is a -regular ultrafilter, then either
- (a)
- is -regular, or
- (b)
- the cofinality of the linear order is , and is -regular for all .
14.
Lá szló Zsidó 《Proceedings of the American Mathematical Society》2000,128(7):2001-2006
The goal of the paper is to prove the following theorem: if , are unital -algebras, simple and nuclear, then any -subalgebra of the -tensor product of and , which contains the tensor product of with the scalar multiples of the unit of , splits in the -tensor product of with some -subalgebra of .
15.
Multidimensional analogues of Bohr's theorem on power series 总被引:2,自引:0,他引:2
Lev Aizenberg 《Proceedings of the American Mathematical Society》2000,128(4):1147-1155
Generalizing the classical result of Bohr, we show that if an -variable power series converges in -circular bounded complete domain and its sum has modulus less than 1, then the sum of the maximum of the modulii of the terms is less than 1 in the homothetic domain , where . This constant is near to the best one for the domain
16.
Uri Elias 《Proceedings of the American Mathematical Society》2000,128(2):475-484
This work compares the solutions of an th order differential inequality plus boundary conditions with the solution of the related differential equation with boundary conditions. The differential operator is assumed to be disconjugate. It is proved that under suitable conditions the ratio of these solutions is monotone. The solution of the inequality can be replaced by the corresponding Green's function.
17.
Let be a graph. We determine all graphs which are -like. We also prove that if are graphs, then in order that each -like continuum be -indecomposable for some it is necessary and sufficient that if is a graph, then is not -like for some integer with . This generalizes a well known theorem of Burgess.
18.
Let be a smooth involution on a closed -dimensional manifold such that all Stiefel-Whitney classes of the tangent bundle to each component of the fixed point set of vanish in positive dimension. In this paper, we estimate the least possible lower bound of dim if does not bound.
19.
Hisao Taya 《Proceedings of the American Mathematical Society》2000,128(5):1285-1292
Let be a square-free integer with and . Put and . For the cyclotomic -extension of , we denote by the -th layer of over . We prove that the -Sylow subgroup of the ideal class group of is trivial for all integers if and only if the class number of is not divisible by the prime . This enables us to show that there exist infinitely many real quadratic fields in which splits and whose Iwasawa -invariant vanishes.
20.
Cristian D. Gonzalez-Avilé s 《Proceedings of the American Mathematical Society》2000,128(4):953-961
Let be a finite Galois extension of number fields with Galois group , let be an abelian variety defined over , and let and denote, respectively, the Tate-Shafarevich groups of over and of over . Assuming that these groups are finite, we derive, under certain restrictions on and , a formula for the order of the subgroup of of -invariant elements. As a corollary, we obtain a simple formula relating the orders of , and when is a quadratic extension and is the twist of by the non-trivial character of .