共查询到20条相似文献,搜索用时 46 毫秒
1.
Reza Sazeedeh 《Proceedings of the American Mathematical Society》2007,135(8):2339-2345
Let be a Noetherian homogeneous ring with local base ring and let be a finitely generated graded -module. Let be the largest integer such that is not Artinian. We will prove that are Artinian for all and there exists a polynomial of degree less than such that for all . Let be the first integer such that the local cohomology module is not cofinite. We will show that for all the graded module is Artinian.
2.
Mara D. Neusel Mü fit Sezer 《Proceedings of the American Mathematical Society》2007,135(8):2347-2354
Let be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map In our 2005 paper it has been shown that the Noether map is surjective if is a projective -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .
3.
Let be a compact metric space and let be a real number with The aim of this paper is to solve a linear preserver problem on the Banach algebra of Hölder functions of order from into We show that each linear bijection having the property that for every where is of the form for every where with is a surjective isometry and is a linear functional.
4.
Francisco-Javier Turiel 《Proceedings of the American Mathematical Society》2007,135(8):2665-2667
We construct, for every even dimensional sphere , , and every odd integer , a homogeneous polynomial map of Brouwer degree and algebraic degree .
5.
Igor Kukavica 《Proceedings of the American Mathematical Society》2007,135(8):2415-2421
We study backward uniqueness properties for equations of the form Under mild regularity assumptions on and , it is shown that implies for . The argument is based on -log and log-log convexity. The results apply to mildly nonlinear parabolic equations and systems with rough coefficients and the 2D Navier-Stokes system.
6.
Dusan Repovs Boaz Tsaban Lyubomyr Zdomskyy 《Proceedings of the American Mathematical Society》2008,136(7):2515-2520
We show that even for subsets of the real line that do not contain perfect sets, the Hurewicz property does not imply the property , asserting that for each countable family of open -covers of , there is a choice function whose image is a -cover of . This settles a problem of Just, Miller, Scheepers, and Szeptycki. Our main result also answers a question of Bartoszyński and the second author, and implies that for , the conjunction of Sakai's strong countable fan tightness and the Reznichenko property does not imply Arhangelskiı's property .
7.
Daria Michalik 《Proceedings of the American Mathematical Society》2007,135(8):2661-2664
We give a short proof of the following fact: the set of embeddings of any -dimensional separable metric space into a certain -dimensional subset of the -product of Sierpinski curves is residual in .
8.
Katsuhiko Matsuzaki 《Proceedings of the American Mathematical Society》2007,135(8):2573-2579
For an analytically infinite Riemann surface , the quasiconformal mapping class group always acts faithfully on the ordinary Teichmüller space . However in this paper, an example of is constructed for which acts trivially on its asymptotic Teichmüller space .
9.
Kathleen L. Petersen 《Proceedings of the American Mathematical Society》2008,136(7):2387-2393
Let be a number field with real places and complex places, and let be the ring of integers of . The quotient has cusps, where is the class number of . We show that under the assumption of the generalized Riemann hypothesis that if is not or an imaginary quadratic field and if , then has infinitely many maximal subgroups with cusps. A key element in the proof is a connection to Artin's Primitive Root Conjecture.
10.
A radical extension of the rational numbers is a field generated by an element having a power in , and a cyclotomic extension is an extension generated by a root of unity. We show that a radical extension that is almost Galois over is almost cyclotomic. More precisely, we prove that if is radical with Galois closure , then contains a cyclotomic field such that the degree is bounded above by an almost linear function of . In particular, if is Galois, it contains a cyclotomic field such that .
11.
We consider an invertible operator on a Banach space whose spectrum is an interpolating set for Hölder classes. We show that if , , with and , then for all , assuming that satisfies suitable regularity conditions. When is a Hilbert space and (i.e. is a contraction), we show that under the same assumptions, is unitary and this is sharp.
12.
B. P. Duggal 《Proceedings of the American Mathematical Society》2007,135(9):2899-2905
A Banach space operator is completely hereditarily normaloid, , if either every part, and (also) for every invertible part , of is normaloid or if for every complex number every part of is normaloid. Sufficient conditions for the perturbation of by an algebraic operator to satisfy Weyl's theorem are proved. Our sufficient conditions lead us to the conclusion that the conjugate operator satisfies -Weyl's theorem.
13.
Vigleik Angeltveit 《Proceedings of the American Mathematical Society》2008,136(7):2323-2332
We define the notion of an enriched Reedy category and show that if is a -Reedy category for some symmetric monoidal model category and is a -model category, the category of -functors and -natural transformations from to is again a model category.
14.
Anders J. Frankild Sean Sather-Wagstaff 《Proceedings of the American Mathematical Society》2008,136(7):2303-2312
Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following result. Let be a commutative noetherian ring and an ideal in the Jacobson radical of . Let be the -adic completion of . If is a finitely generated -module such that for all , then is -adically complete.
15.
Esteban Andruchow Lá zaro Recht Alejandro Varela 《Proceedings of the American Mathematical Society》2007,135(8):2527-2537
We consider the problem of finding short smooth curves of isometries in a Hilbert space . The length of a smooth curve , , is measured by means of , where denotes the usual norm of operators. The initial value problem is solved: for any isometry and each tangent vector at (which is an operator of the form with ) with norm less than or equal to , there exist curves of the form , with initial velocity , which are short along their path. These curves, which we call metric geodesics, need not be unique, and correspond to the so called extension problem considered by M.G. Krein and others: in our context, given a symmetric operator find all possible extending to all , with . We also consider the problem of finding metric geodesics joining two given isometries and . It is well known that if there exists a continuous path joining and , then both ranges have the same codimension. We show that if this number is finite, then there exist metric geodesics joining and .
16.
Nicholas Proudfoot 《Proceedings of the American Mathematical Society》2007,135(12):3989-3994
Given a hyperplane arrangement in a real vector space , we introduce a real algebraic prevariety , and exhibit the complement of in the complexification of as the total space of an affine bundle over with fibers modeled on the dual vector space .
17.
M. C. Stanley 《Proceedings of the American Mathematical Society》2007,135(8):2619-2622
In , assume that is a strong limit cardinal and . Let be the set of approachable ordinals less than . An open question of M. Foreman is whether can be non-stationary in some and preserving extension of . It is shown here that if is such an outer model, then is infinite, for each positive integer .
18.
Let be a finite system of residue classes which forms an -cover of (i.e., every integer belongs to at least members of ). In this paper we show the following sharp result: For any positive integers and , if there is such that the fractional part of is , then there are at least such subsets of . This extends an earlier result of M. Z. Zhang and an extension by Z. W. Sun. Also, we generalize the above result to -covers of the integral ring of any algebraic number field with a power integral basis.
19.
Amol Sasane 《Proceedings of the American Mathematical Society》2007,135(7):2107-2111
Let , denote the unit disc and unit circle, respectively, in , with center 0. If , then let denote the set of complex-valued functions defined on that are analytic in , and continuous and bounded on . Then is a ring with pointwise addition and multiplication. We prove that if the intersection of with the set of limit points of is not empty, then the ring is not coherent.
20.
A. Giannopoulos A. Pajor G. Paouris 《Proceedings of the American Mathematical Society》2007,135(8):2599-2606
We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If is a convex body in with volume one and center of mass at the origin, there exists such that for all , where is an absolute constant. The proof is based on the study of the -centroid bodies of . Analogous results hold true for general log-concave measures.