共查询到20条相似文献,搜索用时 31 毫秒
1.
Y. Bahturin A. Giambruno M. Zaicev 《Proceedings of the American Mathematical Society》1999,127(1):63-69
Let be an algebra over a field and a finite group of automorphisms and anti-automorphisms of . We prove that if satisfies an essential -polynomial identity of degree , then the -codimensions of are exponentially bounded and satisfies a polynomial identity whose degree is bounded by an explicit function of . As a consequence we show that if is an algebra with involution satisfying a -polynomial identity of degree , then the -codimensions of are exponentially bounded; this gives a new proof of a theorem of Amitsur stating that in this case must satisfy a polynomial identity and we can now give an upper bound on the degree of this identity.
2.
We investigate the existence of principal eigenvalues (i.e., eigenvalues corresponding to positive eigenfunctions) for the boundary value problem on ; on , where is a bounded region in , is an indefinite weight function and may be positive, negative or zero.
3.
The main theorem says that any module-finite (but not necessarily commutative) algebra over a commutative Noetherian universally catenary ring is catenary. Hence the ring is catenary if is Cohen-Macaulay. When is local and is a Cohen-Macaulay -module, we have that is a catenary ring, for any , and the equality holds true for any pair of prime ideals in and for any saturated chain of prime ideals between and .
4.
Open covers and partition relations 总被引:1,自引:0,他引:1
Marion Scheepers 《Proceedings of the American Mathematical Society》1999,127(2):577-581
An open cover of a topological space is said to be an -cover if there is for each finite subset of the space a member of the cover which contains the finite set, but the space itself is not a member of the cover. We prove theorems which imply that a set of real numbers has Rothberger's property if, and only if, for each positive integer , for each -cover of , and for each function from the two-element subsets of , there is a subset of such that is constant on , and each element of belongs to infinitely many elements of (Theorem 1). A similar characterization is given of Menger's property for sets of real numbers (Theorem 6).
5.
Konrad J. Swanepoel 《Proceedings of the American Mathematical Society》1999,127(7):2155-2162
A hollow axis-aligned box is the boundary of the cartesian product of compact intervals in . We show that for , if any of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any of a collection of hollow axis-aligned rectangles in have non-empty intersection, then the whole collection has non-empty intersection. The values for and for are the best possible in general. We also characterize the collections of hollow boxes which would be counterexamples if were lowered to , and to , respectively.
6.
Sy D. Friedman 《Proceedings of the American Mathematical Society》1999,127(12):3707-3709
We use ``iterated square sequences' to show that there is an -definable partition such that if is an inner model not containing :
- (a)
- For some is stationary.
- (b)
- For each there is a generic extension of in which does not exist and is non-stationary.
7.
L. Mattner 《Proceedings of the American Mathematical Society》1999,127(6):1847-1854
There exists an asymmetric probability measure on the real line with for every . can be chosen absolutely continuous and can be chosen to be concentrated on the integers. In both cases, can be chosen to have moments of every order, but cannot be determined by its moments.
8.
Nobuhiko Fujii Akihiro Nakamura Ray Redheffer 《Proceedings of the American Mathematical Society》1999,127(6):1815-1818
For let be complex numbers such that is bounded. For define , where . Then the excesses in the sense of Paley and Wiener satisfy .
9.
Ian M. Musson 《Proceedings of the American Mathematical Society》1999,127(10):2821-2827
Let be the Lie superalgebra . We show that there is a surjective homomorphism from to the Weyl algebra , and we use this to construct an analog of the Joseph ideal. We also obtain a decomposition of the adjoint representation of on and use this to show that if is made into a Lie superalgebra using its natural -grading, then . In addition, we show that if and are isomorphic as Lie superalgebras, then . This answers a question of S. Montgomery.
10.
Greg Hjorth 《Proceedings of the American Mathematical Society》1999,127(1):271-278
Let be a Polish group, a Polish topology on a space , acting continuously on , with -invariant and in the Borel algebra generated by . Then there is a larger Polish topology on so that is open with respect to , still acts continuously on , and has a basis consisting of sets that are of the same Borel rank as relative to .
11.
Let be a module finite extension of normal domains. We show that if is unramified in codimension one and if has finite projective dimension over , then is étale over . Our proof makes use of P. Roberts' New Intersection Theorem.
12.
Let be a non-trivial finite Galois extension of a field . In this paper we investigate the role that valuation-theoretic properties of play in determining the non-triviality of the relative Brauer group, , of over . In particular, we show that when is finitely generated of transcendence degree 1 over a -adic field and is a prime dividing , then the following conditions are equivalent: (i) the -primary component, , is non-trivial, (ii) is infinite, and (iii) there exists a valuation of trivial on such that divides the order of the decomposition group of at .
13.
The Furuta inequality with negative powers 总被引:2,自引:0,他引:2
Let be bounded linear operators on a Hilbert space satisfying . Furuta showed the operator inequality
as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.
as long as positive real numbers satisfy and . In this paper, we show this inequality is valid if negative real numbers satisfy a certain condition. Also, we investigate the optimality of that condition.
14.
Piotr Pawlowski 《Proceedings of the American Mathematical Society》1999,127(5):1493-1497
Let be a complex polynomial of degree having zeros in a disk . We deal with the problem of finding the smallest concentric disk containing zeros of . We obtain some estimates on the radius of this disk in general as well as in the special case, where zeros in are isolated from the other zeros of . We indicate an application to the root-finding algorithms.
15.
Yakov Berkovich 《Proceedings of the American Mathematical Society》1999,127(9):2505-2509
For a prime divisor of the order of a finite group , we present the set of -subgroups generating . In particular, we present the set of primary subgroups of generating the last member of the lower central series of . The proof is based on the Frobenius Normal -Complement Theorem and basic properties of minimal nonnilpotent groups. Let be a group and a group-theoretic property inherited by subgroups and epimorphic images such that all minimal non--subgroups (-subgroups) of are not nilpotent. Then (see the lemma), if is generated by all -subgroups of it follows that is a -group.
16.
J. Marshall Ash Michael Ganzburg 《Proceedings of the American Mathematical Society》1999,127(1):211-216
Let be a trigonometric polynomial of degree The problem of finding the largest value for in the inequality is studied. We find exactly provided is the conjugate of an even integer and For general we get an interval estimate for where the interval length tends to as tends to
17.
Luis Bernal-Gonzá lez 《Proceedings of the American Mathematical Society》1999,127(11):3279-3285
We prove in this paper that if is a hereditarily hypercyclic sequence of continuous linear mappings between two topological vector spaces and , where is metrizable, then there is an infinite-dimensional linear submanifold of such that each non-zero vector of is hypercyclic for . If, in addition, is metrizable and separable and is densely hereditarily hypercyclic, then can be chosen dense.
18.
Li Jiankui 《Proceedings of the American Mathematical Society》1999,127(1):235-239
In this paper, we prove that if is an -dimensional subspace of , then is -reflexive, where denotes the greatest integer not larger than . By the result, we show that if is an elementary operator on a -algebra , then is completely positive if and only if is -positive.
19.
Mong-Lung Lang Ser-Peow Tan 《Proceedings of the American Mathematical Society》1999,127(11):3131-3140
Let cos and let be the Hecke group associated to . In this article, we show that for a prime ideal in , the congruence subgroups of are self-normalized in .
20.
We study real algebraic morphisms from nonsingular real algebraic varieties with into nonsingular real algebraic curves . We show, among other things, that the set of real algebraic morphisms from into is never dense in the space of all maps from into , unless is biregularly isomorphic to a Zariski open subset of the unit circle.