共查询到20条相似文献,搜索用时 46 毫秒
1.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(7):1955-1961
Let be a global function field, a degree one prime divisor of and let be the Dedekind domain of functions in regular outside . Let be the Hilbert class field of , the integral closure of in . Let be a rank one normalized Drinfeld -module and let be a prime ideal in . We explicitly determine the finite -module structure of . In particular, if , is an odd prime number and is the Carlitz -module, then the finite -module is always cyclic.
2.
B. P. Duggal 《Proceedings of the American Mathematical Society》1998,126(7):2047-2052
Given a Hilbert space , let be operators on . Anderson has proved that if is normal and , then for all operators . Using this inequality, Du Hong-Ke has recently shown that if (instead) , then for all operators . In this note we improve the Du Hong-Ke inequality to for all operators . Indeed, we prove the equivalence of Du Hong-Ke and Anderson inequalities, and show that the Du Hong-Ke inequality holds for unitarily invariant norms.
3.
Hisao Kato 《Proceedings of the American Mathematical Society》1998,126(7):2151-2157
The measure of scrambled sets of interval self-maps was studied by many authors, including Smítal, Misiurewicz, Bruckner and Hu, and Xiong and Yang. In this note, first we introduce the notion of ``-chaos" which is related to chaos in the sense of Li-Yorke, and we prove a general theorem which is an improvement of a theorem of Kuratowski on independent sets. Second, we apply the result to scrambled sets of higher dimensional cases. In particular, we show that if a map of the unit -cube is -chaotic on , then for any there is a map such that and are topologically conjugate, and has a scrambled set which has Lebesgue measure 1, and hence if , then there is a homeomorphism with a scrambled set satisfying that is an -set in and has Lebesgue measure 1.
4.
M. Jimé nez Sevilla J. P. Moreno 《Proceedings of the American Mathematical Society》1998,126(7):1989-1997
We are concerned in this paper with the density of functionals which do not attain their norms in Banach spaces. Some earlier results given for separable spaces are extended to the nonseparable case. We obtain that a Banach space is reflexive if and only if it satisfies any of the following properties: (i) admits a norm with the Mazur Intersection Property and the set of all norm attaining functionals of contains an open set, (ii) the set of all norm one elements of contains a (relative) weak* open set of the unit sphere, (iii) has and contains a (relative) weak open set of the unit sphere, (iv) is , has and contains a (relative) weak open set of the unit sphere. Finally, if is separable, then is reflexive if and only if contains a (relative) weak open set of the unit sphere.
5.
Gary L. Peterson 《Proceedings of the American Mathematical Society》1998,126(7):1897-1900
Suppose and are endomorphism near-rings generated by
groups of automorphisms containing the inner automorphisms of two respective finite perfect groups and . In this note we show that if and are isomorphic, then and are isomorphic.
groups of automorphisms containing the inner automorphisms of two respective finite perfect groups and . In this note we show that if and are isomorphic, then and are isomorphic.
6.
Mark L. Lewis 《Proceedings of the American Mathematical Society》1998,126(7):1915-1921
Let be a finite solvable group. Assume that the degree graph of has exactly two connected components that do not contain . Suppose that one of these connected components contains the subset , where and are coprime when . Then the derived length of is less than or equal to .
7.
Peter M. Schuster 《Proceedings of the American Mathematical Society》1998,126(7):1983-1987
We construct a space of fine moduli for the substructures of an arbitrary compact complex space . A substructure of is given by a subalgebra of the structure sheaf with the additional feature that is also a complex space; and are called equivalent if and only if and are isomorphic as subalgebras of .
Since substructures are quotients, it is only natural to start with the fine moduli space of all complex-analytic quotients of . In order to obtain a representable moduli functor of substructures, we are forced to concentrate on families of quotients which satisfy some flatness condition for relative differential modules of higher order. Considering the corresponding flatification of , we realize that its open subset consisting of all substructures turns out to be a complex space which has the required universal property.
8.
Arjeh M. Cohen Bruce N. Cooperstein 《Proceedings of the American Mathematical Society》1998,126(7):2095-2102
The homogeneous space , where is a simple algebraic group and a parabolic subgroup corresponding to a fundamental weight (with respect to a fixed Borel subgroup of in ), is known in at least two settings. On the one hand, it is a projective variety, embedded in the projective space corresponding to the representation with highest weight . On the other hand, in synthetic geometry, is furnished with certain subsets, called lines, of the form where is a preimage in of the fundamental reflection corresponding to and . The result is called the Lie incidence structure on . The lines are projective lines in the projective embedding. In this paper we investigate to what extent the projective variety data determines the Lie incidence structure.
9.
Shreeram S. Abhyankar Paul A. Loomis 《Proceedings of the American Mathematical Society》1998,126(7):1885-1896
In a previous paper, nice quintinomial equations were given for unramified coverings of the affine line in nonzero characteristic with the projective symplectic isometry group PSp and the (vectorial) symplectic isometry group Sp as Galois groups where is any integer and is any power of . Here we deform these equations to get nice quintinomial equations for unramified coverings of the once punctured affine line in characteristic with the projective symplectic similitude group PGSp and the (vectorial) symplectic similitude group GSp as Galois groups.
10.
P. R. Hewitt 《Proceedings of the American Mathematical Society》1998,126(7):1909-1914
Let be a group, let be a field, and let be a local system - an upwardly directed collection of subgroups whose union is . In this paper we give a short, elementary proof of the following result: If either is a --bimodule, or else is finite dimensional over its center, then . From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.
11.
Paul C. Eklof Saharon Shelah 《Proceedings of the American Mathematical Society》1998,126(7):1901-1907
We answer a long-standing open question by proving in ordinary set theory, ZFC, that the Kaplansky test problems have negative answers for -separable abelian groups of cardinality . In fact, there is an -separable abelian group such that is isomorphic to but not to . We also derive some relevant information about the endomorphism ring of .
12.
Eiji Ogasa 《Proceedings of the American Mathematical Society》1998,126(7):2175-2182
We prove that, for any ordinary sense slice 1-link , we can define the Arf invariant, and Arf()=0. We prove that, for any -component 1-link , there exists a -component ordinary sense slice 1-link of which is a sublink.
13.
Dimitar K. Dimitrov 《Proceedings of the American Mathematical Society》1998,126(7):2065-2070
The classical Gauss-Lucas Theorem states that all the critical points (zeros of the derivative) of a nonconstant polynomial lie in the convex hull of the zeros of . It is proved that, actually, a subdomain of contains the critical points of .
14.
Theodore A. Slaman 《Proceedings of the American Mathematical Society》1998,126(7):2117-2122
There is a countable first order structure such that for any set of integers , is not recursive if and only if there is a presentation of which is recursive in .
15.
Saban Alaca 《Proceedings of the American Mathematical Society》1998,126(7):1949-1953
A -integral basis of a cubic field is determined for each rational prime , and then an integral basis of and its discriminant are obtained from its -integral bases.
16.
Victoria Paolantoni 《Proceedings of the American Mathematical Society》1998,126(6):1733-1738
Let be a smooth real hypersurface of and a compact submanifold of . We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on and , an estimate of the submeanvalue on of any function on a neighbourhood of , by the norm of on a neighbourhood of in .
17.
B. Shapiro 《Proceedings of the American Mathematical Society》1998,126(7):1923-1930
For a given real generic curve let denote the ruled hypersurface in consisting of all osculating subspaces to of codimension 2. In this note we show that for any two convex real projective curves and the pairs and are homeomorphic.
18.
Dave Witte 《Proceedings of the American Mathematical Society》1998,126(4):1005-1015
Let and be matrices of determinant over a field , with or . We show that if is not a scalar matrix, then is a product of matrices similar to . Analogously, we conjecture that if and are elements of a semisimple algebraic group over a field of characteristic zero, and if there is no normal subgroup of containing but not , then is a product of conjugates of . The conjecture is verified for orthogonal groups and symplectic groups, and for all semisimple groups over local fields. Thus, in a connected, semisimple Lie group with finite center, the only conjugation-invariant subsemigroups are the normal subgroups.
19.
Jeffrey Bergen D. S. Passman 《Proceedings of the American Mathematical Society》1998,126(6):1627-1635
Let be a finite abelian group and let be a, possibly restricted, -graded Lie color algebra. Then the enveloping algebra is also -graded, and we consider the question of whether being graded-prime implies that it is prime. The first section of this paper is devoted to the special case of Lie superalgebras over a field of characteristic . Specifically, we show that if and if has a unique minimal graded-prime ideal, then this ideal is necessarily prime. As will be apparent, the latter result follows quickly from the existence of an anti-automorphism of whose square is the automorphism of the enveloping algebra associated with its -grading. The second section, which is independent of the first, studies more general Lie color algebras and shows that if is graded-prime and if most homogeneous components of are infinite dimensional over , then is prime. Here we use -methods to study the grading on the extended centroid of . In particular, if is generated by the infinite support of , then we prove that is homogeneous.
20.
B. A. Sethuraman 《Proceedings of the American Mathematical Society》1998,126(1):9-14
Let , where is a prime, and . In , let be the variety defined by . We show that any subvariety of of codimension less than must have degree a multiple of . We also show that the bounds on the codimension in our results are strict by exhibiting subvarieties of the appropriate codimension whose degrees are prime to .