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1.
Assume that is a finite-dimensional Hopf algebra over a field and that is an -module algebra satisfying a polynomial identity (PI). We prove that if is semisimple and is -semiprime, then is semiprime. If is cosemisimple, we show that the prime radical of is -stable.
2.
Takateru Okayasu Yasunori Ueta 《Proceedings of the American Mathematical Society》2007,135(5):1399-1403
We will give some sufficient conditions for a -hyponormal operator, , to be normal, and a sufficient condition for a triplet of operators , , with , self-adjoint and unitary such that necessarily satisfies .
3.
Georgia Benkart Paul Terwilliger 《Proceedings of the American Mathematical Society》2007,135(6):1659-1668
We consider the three-point loop algebra, where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.
4.
G. Bouchitté C. Jimenez M. Rajesh 《Proceedings of the American Mathematical Society》2007,135(11):3525-3535
Let be a bounded Lipschitz regular open subset of and let be two probablity measures on . It is well known that if is absolutely continuous, then there exists, for every , a unique transport map pushing forward on and which realizes the Monge-Kantorovich distance . In this paper, we establish an bound for the displacement map which depends only on , on the shape of and on the essential infimum of the density .
5.
Lindsay N. Childs 《Proceedings of the American Mathematical Society》2007,135(11):3453-3460
Let be an odd prime, , the elementary abelian -group of rank , and let be the group of principal units of the ring . If is a Galois extension with Galois group , then we show that for , the number of Hopf Galois structures on afforded by -Hopf algebras with associated group is greater than , where .
6.
J. Berkovits 《Proceedings of the American Mathematical Society》2007,135(7):2059-2064
The reduction theorem for the Leray-Schauder degree provides an efficient tool to calculate the value of the degree in a suitable invariant subspace. We shall prove how the calculation of the value of the topological degree for a mapping of class from a real separable reflexive Banach space into the dual space can be reduced into the calculation of degree of mapping from a closed subspace into Since the Leray-Schauder mappings are acting from to and we are dealing with mappings from to the standard `invariant subspace' condition must be replaced by a less obvious one.
7.
Jared Schlieper 《Proceedings of the American Mathematical Society》2007,135(7):2081-2088
The concept of an intersection body is central for the dual Brunn-Minkowski theory and has also played an important role in the solution of the Busemann-Petty problem. A more general concept of -intersection bodies is related to the generalization of the Busemann-Petty problem. In this note, we compare classes of -intersection bodies for different and examine the conjecture that these classes increase with . In particular, we construct a -intersection body that is not a -intersection body.
8.
Let be a -group with generator , and let be a local -semigroup commuting with . Then the operators , , form a local -semigroup. It is proved that if is injective and is the generator of , then is closable and is the generator of . Also proved are a characterization theorem for local -semigroups with not necessarily injective and a theorem about solvability of the abstract inhomogeneous Cauchy problem:
9.
We prove that all -cotilting -modules are pure-injective for any ring and any . To achieve this, we prove that is a covering class whenever is an -module such that is closed under products and pure submodules.
10.
David Schrittesser 《Proceedings of the American Mathematical Society》2007,135(4):1213-1222
-absoluteness for forcing means that for any forcing , . `` inaccessible to reals' means that for any real , . To measure the exact consistency strength of `` -absoluteness for forcing and is inaccessible to reals', we introduce a weak version of a weakly compact cardinal, namely, a (lightface) -indescribable cardinal; has this property exactly if it is inaccessible and .
11.
Mohsen Pourahmadi Akihiko Inoue Yukio Kasahara 《Proceedings of the American Mathematical Society》2007,135(4):1233-1239
For a nonnegative integrable weight function on the unit circle , we provide an expression for , in terms of the series coefficients of the outer function of , for the weighted distance , where is the normalized Lebesgue measure and ranges over trigonometric polynomials with frequencies in , , . The problem is open for .
12.
In this paper some upper bounds for the volume and diameter of central sections of symmetric convex bodies are obtained in terms of the isotropy constant of the polar body. The main consequence is that every symmetric convex body in of volume one has a proportional section , dim ( ), of diameter bounded by whenever the polar body is in isotropic position ( is some absolute constant).
13.
Jongil Park 《Proceedings of the American Mathematical Society》2007,135(7):2301-2307
In this article, for each finitely presented group , we construct a family of minimal symplectic -manifolds with which cover most lattice points with large in the region . Furthermore, we show that all these -manifolds admit infinitely many distinct smooth structures.
14.
Yifeng Xue 《Proceedings of the American Mathematical Society》2007,135(3):705-711
A unital -algebra is said to have the (APD)-property if every nonzero element in has the approximate polar decomposition. Let be a closed ideal of . Suppose that and have (APD). In this paper, we give a necessary and sufficient condition that makes have (APD). Furthermore, we show that if and or is a simple purely infinite -algebra, then has (APD).
15.
Muharem Avdispahic Lejla Smajlovic 《Proceedings of the American Mathematical Society》2006,134(7):2125-2130
A. Magyar's result on -bounds for a family of operators on -spheres () in is improved to match the corresponding theorem for -spheres.
16.
Margarida Mendes Lopes Rita Pardini 《Proceedings of the American Mathematical Society》2007,135(5):1279-1282
In this note it is shown that, given a smooth minimal complex surface of general type with , , for which the bicanonical map is a morphism, the degree of is not 3. This completes our earlier results, showing that if is a minimal surface of general type with , such that is free, then the bicanonical map of can have degree 1, 2 or 4.
17.
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.
18.
Roberto Johnson José Pantoja 《Proceedings of the American Mathematical Society》2007,135(2):579-586
Let be a non-archimedean local field with odd residual characteristic. Let be the group We construct explicit Whittaker models for any supercuspidal representation of with positive level.
19.
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 .
20.
In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.