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1.
Katsuro Sakai 《Proceedings of the American Mathematical Society》1997,125(9):2809-2813
Let be the -dimensional universal Menger compactum, a -set in and a metrizable zero-dimensional compact group with the unit. It is proved that there exists a semi-free -action on such that is the fixed point set of every . As a corollary, it follows that each compactum with can be embedded in as the fixed point set of some semi-free -action on .
2.
James Cummings 《Proceedings of the American Mathematical Society》1997,125(9):2703-2709
Let be a singular cardinal in , and let be a model such that for some -cardinal with . We apply Shelah's pcf theory to study this situation, and prove the following results. 1) is not a -c.c generic extension of . 2) There is no ``good scale for ' in , so in particular weak forms of square must fail at . 3) If then and also . 4) If then .
3.
Gert K. Pedersen 《Proceedings of the American Mathematical Society》1997,125(9):2657-2660
Given a pair , of -commuting, hereditary -subalgebras of a unital -algebra , such that is -unital and , there is an element in , with , such that is strictly positive in and is strictly positive in in . Moreover, is strictly positive in in .
4.
Peter Danchev 《Proceedings of the American Mathematical Society》1997,125(9):2559-2564
In this note we study the commutative modular and semisimple group rings of -summable abelian -groups, which group class was introduced by R. Linton and Ch. Megibben. It is proved that is -summable if and only if is -summable, provided is an abelian group and is a commutative ring with 1 of prime characteristic , having a trivial nilradical. If is a -summable -group and the group algebras and over a field of characteristic are -isomorphic, then is a -summable -group, too. In particular provided is totally projective of a countable length.
Moreover, when is a first kind field with respect to and is -torsion, is -summable if and only if is a direct sum of cyclic groups.
5.
Huaxin Lin 《Proceedings of the American Mathematical Society》1997,125(9):2671-2676
We show that a separable -algebra of type I has real rank zero if and only if where is a modified dimension. We also show that a separable -algebra of type I has real rank zero if and only if it is an AF-algebra.
6.
Robert Gilmer William Heinzer 《Proceedings of the American Mathematical Society》1997,125(9):2513-2520
Let be a local (Noetherian) ring. The main result of this paper asserts the existence of a local extension ring of such that (i) dominates , (ii) the residue field of is a finite purely transcendental extension of , (iii) every associated prime of (0) in contracts in to an associated prime of (0), and (iv) . In addition, it is shown that can be obtained so that either is the maximal ideal of or is a localization of a finitely generated -algebra.
7.
Marion Scheepers 《Proceedings of the American Mathematical Society》1997,125(9):2719-2724
An open cover of an infinite separable metric space is an -cover of if and for every finite subset of there is a such that . Let be the collection of -covers of . We show that the partition relation holds if, and only if, the partition relation holds.
8.
A. Edward Nussbaum 《Proceedings of the American Mathematical Society》1997,125(12):3541-3545
Let and be semibounded (bounded from below) operators in a Hilbert space and a dense linear manifold contained in the domains of , , , and , and such that for all in . It is shown that if the restriction of to is essentially self-adjoint, then and are essentially self-adjoint and and commute, i.e. their spectral projections permute.
9.
Peter Schauenburg 《Proceedings of the American Mathematical Society》1997,125(1):83-85
Let be a commutative ring. Assume that is a -bialgebra, and is an -Galois extension of its coinvariant subalgebra . Provided is faithfully flat over , we show that is necessarily a Hopf algebra.
10.
Liangqing Li 《Proceedings of the American Mathematical Society》1997,125(9):2637-2642
In this note, we will disprove the following conjecture raised by Exel-Loring: Let be a -algebra with trace and let be a determinant associated to . If is a continuous family of homomorphisms and is the canonical matrix valued function on which represents the Bott element in , then . It should be noticed that the conjecture has been proved by Exel-Loring for the case that is a smooth family of homomorphisms.
11.
Luis Paris 《Proceedings of the American Mathematical Society》1997,125(3):731-738
Let be a Coxeter system, and let be a subset of . The subgroup of generated by is denoted by and is called a parabolic subgroup. We give the precise definition of the commensurator of a subgroup in a group. In particular, the commensurator of in is the subgroup of in such that has finite index in both and . The subgroup can be decomposed in the form where is finite and all the irreducible components of are infinite. Let be the set of in such that for all . We prove that the commensurator of is . In particular, the commensurator of a parabolic subgroup is a parabolic subgroup, and is its own commensurator if and only if .
12.
Claude Laflamme 《Proceedings of the American Mathematical Society》1997,125(10):3019-3025
We discuss F filters and show that the minimum size of a filter base generating an undiagonalizable filter included in some F filter is the better known bounded evasion number . An application to -sets from trigonometric series is given by showing that if is an -set and has size less than , then is again an -set.
13.
Michael Levin Yaki Sternfeld 《Proceedings of the American Mathematical Society》1997,125(9):2771-2775
Let be a metric continuum and let denote the space of subcontinua of with the Hausdorff metric. We settle a longstanding problem showing that if then . The special structure and properties of hereditarily indecomposable continua are applied in the proof.
14.
Ju Seon Kim 《Proceedings of the American Mathematical Society》1997,125(5):1497-1501
Let be a hypersurface in , and let denote the mean curvature and the scalar curvature of respectively. We show that if is compact and , then is diffeomorphic to . Also we prove that if is complete, is constant and , then is or or .
15.
Let be a Banach -algebra with an identity. Necessary and sufficient conditions are given for to be commutative modulo its -radical and for to be commutative if has a faithful -representation as operators on a Hilbert space.
16.
Peter Semrl 《Proceedings of the American Mathematical Society》1997,125(9):2677-2680
Let be an algebra. A mapping is called a -local automorphism if for every there is an automorphism , depending on and , such that and (no linearity, surjectivity or continuity of is assumed). Let be an infinite-dimensional separable Hilbert space, and let be the algebra of all linear bounded operators on . Then every -local automorphism is an automorphism. An analogous result is obtained for derivations.
17.
Changyu Xia 《Proceedings of the American Mathematical Society》1997,125(6):1801-1806
Let be an ()-dimensional compact Riemannian manifold with nonnegative Ricci curvature and nonempty boundary . Assume that the principal curvatures of are bounded from below by a positive constant . In this paper, we prove that the first nonzero eigenvalue of the Laplacian of acting on functions on satisfies with equality holding if and only if is isometric to an -dimensional Euclidean ball of radius . Some related rigidity theorems for are also proved.
18.
Marion Scheepers 《Proceedings of the American Mathematical Society》1997,125(9):2789-2795
has the monotonic sequence selection property if there is for each , and for every sequence where for each is a sequence converging pointwise monotonically to , a sequence such that for each is a term of , and converges pointwise to . We prove a theorem which implies for metric spaces that has the monotonic sequence selection property if, and only if, has a covering property of Hurewicz.
19.
Gennady Lyubeznik 《Proceedings of the American Mathematical Society》1997,125(7):1941-1944
We show that for fixed and the set of Bernstein-Sato polynomials of all the polynomials in at most variables of degrees at most is finite. As a corollary, we show that there exists an integer depending only on and such that generates as a module over the ring of the -linear differential operators of , where is an arbitrary field of characteristic 0, is the ring of polynomials in variables over and is an arbitrary non-zero polynomial of degree at most .
20.
Gabriel P. Paternain 《Proceedings of the American Mathematical Society》1997,125(9):2759-2765
Let be the total space of a fibre bundle with base a simply connected manifold whose loop space homology grows exponentially for a given coefficient field. Then we show that for any Riemannian metric on , the topological entropy of the geodesic flow of is positive. It follows then, that there exist closed manifolds with arbitrary fundamental group, for which the geodesic flow of any Riemannian metric on has positive topological entropy.