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1.
Let be an algebraically closed field of characteristic the ring of Witt vectors and a complete discrete valuation ring dominating and containing a primitive -th root of unity. Let denote a uniformizing parameter for We study order automorphisms of the formal power series ring which are defined by a series
The set of fixed points of is denoted by and we suppose that they are -rational and that for Let be the minimal semi-stable model of the -adic open disc over in which specializes to distinct smooth points. We study the differential data that can be associated to each irreducible component of the special fibre of Using this data we show that if , then the fixed points are equidistant, and that there are only a finite number of conjugacy classes of order automorphisms in which are not the identity
2.
M. N'Kanza 《Proceedings of the American Mathematical Society》1999,127(9):2587-2590
Here we give new examples of fields in characteristic whose -invariant and -invariant are different: or . These fields are also -fields.
RSUM. Nous donnons ici de nouveaux exemples de corps en caractéristique dont le -invariant et le -invariant diffèrent. Plus précisément: et ou . Ces corps sont aussi des -corps.
3.
Eungil Ko 《Proceedings of the American Mathematical Society》2000,128(3):775-780
In this paper we show that -hyponormal operators with are subscalar. As a corollary, we get that such operators with rich spectra have non-trivial invariant subspaces.
4.
Jutta Hausen Phillip Schultz 《Proceedings of the American Mathematical Society》1998,126(9):2525-2533
Let be a prime number and let be an abelian -group. Let be the maximal normal -subgroup of and the maximal -subgroup of its centre. Let be the torsion radical of . Then . The result is new for and 3, and the proof is new and valid for all primes .
5.
Sergei Yu. Vasilovsky 《Proceedings of the American Mathematical Society》1999,127(12):3517-3524
The algebra of all matrices over a field has a natural -grading . In this paper graded identities of the -graded algebra over a field of characteristic zero are studied. It is shown that all the -graded polynomial identities of follow from the following:
6.
William Browder Jonathan Pakianathan 《Transactions of the American Mathematical Society》2000,352(6):2659-2688
In this paper we will study the cohomology of a family of -groups associated to -Lie algebras. More precisely, we study a category of -groups which will be equivalent to the category of -bracket algebras (Lie algebras minus the Jacobi identity). We then show that for a group in this category, its -cohomology is that of an elementary abelian -group if and only if it is associated to a Lie algebra.
We then proceed to study the exponent of in the case that is associated to a Lie algebra . To do this, we use the Bockstein spectral sequence and derive a formula that gives in terms of the Lie algebra cohomologies of . We then expand some of these results to a wider category of -groups. In particular, we calculate the cohomology of the -groups which are defined to be the kernel of the mod reduction
7.
Nguyen Minh Chuong Nguyen Van Co 《Proceedings of the American Mathematical Society》1999,127(3):685-694
A proof much simpler than the one given by Bikulov (Investigation of the -adic Green function, Teoret. Mat. Fiz. 87 (1991), 376-390) for properties of the 2-dimensional -adic Green function is shown. By this method one can treat a multidimensional case, and some sharp estimates are obtained.
8.
Marc Troyanov 《Proceedings of the American Mathematical Society》2000,128(2):541-545
We prove in this paper that the equation on a -hyperbolic manifold has a solution with -integrable gradient for any bounded measurable function with compact support.
9.
Tomoaki Ono 《Proceedings of the American Mathematical Society》2000,128(2):353-360
Let be a tower of rings of characteristic . Suppose that is a finitely presented -module. We give necessary and sufficient conditions for the existence of -bases of over . Next, let be a polynomial ring where is a perfect field of characteristic , and let be a regular noetherian subring of containing such that . Suppose that is a free -module. Then, applying the above result to a tower of rings, we shall show that a polynomial of minimal degree in is a -basis of over .
10.
Abdelbaki Boutabaa Alain Escassut 《Proceedings of the American Mathematical Society》1998,126(9):2557-2568
Let be a complete ultrametric algebraically closed field of characteristic zero, and let be the field of meromorphic functions in . For all set in and for all we denote by the subset of : zero of order After studying unique range sets for entire functions in in a previous article, here we consider a similar problem for meromorphic functions by showing, in particular, that, for every , there exist sets of elements in such that, if have the same poles (counting multiplicities), and satisfy , then . We show how to construct such sets.
11.
Thomas S. Weigel 《Transactions of the American Mathematical Society》2000,352(9):4143-4154
In this note we investigate the mod cohomology ring of finite -central groups with a certain extension property. For odd it turns out that the structure of the cohomology ring characterizes this class of groups up to extensions by -groups. For certain examples the cohomology ring can be calculated explicitly. As a by-product one gets an alternative proof of a theorem of M.Lazard which states that the Galois cohomology of a uniformly powerful pro--group of rank is isomorphic to .
12.
Pavel Drá bek Stephen B. Robinson 《Proceedings of the American Mathematical Society》2000,128(3):755-765
We consider resonance problems for the one dimensional -Laplacian, and prove the existence of solutions assuming a standard Landesman-Lazer condition. Our proofs use variational techniques to characterize the eigenvalues, and then to establish the solvability of the given boundary value problem.
13.
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.
14.
Extending an example given by T. Kriete, we develop a class of measures each of which consists of a measure on along with a series of weighted point masses in . This class provides relatively simple examples of measures which have the property that the collection of analytic bounded point evaluations for varies with . The first known measures with this property were recently constructed by J. Thomson.
15.
We prove that for every -hyponormal operator there corresponds a hyponormal operator such that and have ``equal spectral structure". We also prove that every -hyponormal operator is subdecomposable. Then some relevant quasisimilarity results are obtained, including that two quasisimilar -hyponormal operators have equal essential spectra.
16.
A sequence of positive integers is called a -sequence if every integer has at most representations with all in and . A -sequence is also called a -sequence or Sidon sequence. The main result is the following
Theorem. Let be a -sequence and for an integer . Then there is a -sequence of size , where .
Corollary. Let . The interval then contains a -sequence of size , when .
17.
Wang Yanying Wu Zhende Ma Kai 《Proceedings of the American Mathematical Society》2000,128(5):1515-1521
The groups of cobordism classes in the unoriented cobordism group containing a representative admitting a -action with fixed point set of constant codimension are determined.
18.
Vivek Sahai 《Proceedings of the American Mathematical Society》1999,127(11):3201-3213
We discuss few models of the quantum universal enveloping algebra of from the special function point of view. Two sets of such models are given, one acting on the space of functions while the other on the space of -Appell functions. These models are closely related through a -integral transformation. Some interesting identities are obtained.
19.
James K. Deveney David R. Finston 《Proceedings of the American Mathematical Society》2000,128(1):31-38
It has been conjectured that every free algebraic action of the additive group of complex numbers on complex affine three space is conjugate to a global translation. The main result lends support to this conjecture by showing that the morphism to the variety defined by the ring of invariants of the associated action on the coordinate ring is smooth. As a consequence, the graph morphism is an open immersion, and simple proofs of certain cases of the conjecture are obtained.
20.
Let denote the Von Mangoldt function and . We describe an elementary method for computing isolated values of . The complexity of the algorithm is time and space. A table of values of for up to is included, and some times of computation are given.