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1.
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.
2.
A. Matheson 《Proceedings of the American Mathematical Society》1998,126(7):2061-2063
A bounded composition operator on , where is the unit ball in , is Dunford-Pettis if and only if the radial limit function of takes values on the unit sphere only on a set of surface measure zero. A similar theorem holds on bounded strongly pseudoconvex domains with smooth boundary.
3.
Reinhold Hü bl Xiaotao Sun 《Proceedings of the American Mathematical Society》1998,126(7):1931-1940
If is a local Dedekind scheme and is a projective Cohen-Macaulay variety of relative dimension , then is torsionfree if and only if is arithmetically Cohen-Macaulay for a suitable embedding in . If is regular then is torsionfree whenever the multiplicity of the special fibre is not a multiple of the characteristic of the residue class field.
4.
Vicente Palmer 《Proceedings of the American Mathematical Society》1998,126(7):2089-2094
L. Karp and M. Pinsky proved that, for small radius , the mean exit time function of an extrinsic -ball in a hypersurface is bounded from below by the corresponding function defined on an extrinsic -ball in . A counterexample given by C. Mueller proves that this inequality doesn't holds in the large. In this paper we show that, if is convex, then the inequality holds for all radii. Moreover, we characterize the equality and show that analogous results are true in the sphere.
5.
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.
6.
Tadashi Yanai 《Proceedings of the American Mathematical Society》1998,126(8):2221-2228
In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let be a ring, its left Martindale quotient ring and a right ideal of having no nonzero left annihilator. (1) Let be a pointed coalgebra which measures such that the group-like elements of act as automorphisms of . If is prime and for , then . Furthermore, if the action of extends to and if such that , then . (2) Let be an endomorphism of given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If is semiprime and , then .
7.
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.
8.
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.
9.
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.
10.
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 .
11.
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.
12.
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.
13.
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.
14.
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 .
15.
Harold R. Bennett David J. Lutzer 《Proceedings of the American Mathematical Society》1998,126(7):2191-2196
In this paper we use a metric space due to A. H. Stone and one of its completions to construct a linearly ordered topological space that is \v{C}ech complete, has a -closed-discrete dense subset, is perfect, hereditarily paracompact, first-countable, and has the property that each of its subspaces has a -minimal base for its relative topology. However, is not metrizable and is not quasi-developable. The construction of is a point-splitting process that is familiar in ordered spaces, and an orderability theorem of Herrlich is the link between Stone's metric space and our construction.
16.
Changsun Choi 《Proceedings of the American Mathematical Society》1998,126(4):1149-1153
We prove the weak-type inequality , , between a non-negative subharmonic function and an -valued smooth function , defined on an open set containing the closure of a bounded domain in a Euclidean space , satisfying , and , where is a constant. Here is the harmonic measure on with respect to 0. This inequality extends Burkholder's inequality in which and , a Euclidean space.
17.
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.
18.
It is shown that the suspension order of the -fold cartesian product of real projective -space is less than or equal to the suspension order of the -fold symmetric product of and greater than or equal to , where and satisfy and . In particular has suspension order , and for fixed the suspension orders of the spaces are unbounded while their stable suspension orders are constant and equal to .
19.
H. P. Goeters W. J. Wickless 《Proceedings of the American Mathematical Society》1998,126(11):3145-3150
A torsion-free abelian group is if every map from a pure subgroup of into lifts to an endomorphism of The class of groups has been extensively studied, resulting in a number of nice characterizations. We obtain some characterizations for the class of homogeneous groups, those homogeneous groups such that, for pure in every has a lifting to a quasi-endomorphism of An irreducible group is if and only if every pure subgroup of each of its strongly indecomposable quasi-summands is strongly indecomposable. A group is if and only if every endomorphism of is an integral multiple of an automorphism. A group has minimal test for quasi-equivalence ( if whenever and are quasi-isomorphic pure subgroups of then and are equivalent via a quasi-automorphism of For homogeneous groups, we show that in almost all cases the and properties coincide.
20.
Let be a finite -solvable group for different primes and . Let and be such that . We prove that every of -degree has -degree if and only if and .