An effective procedure for minimal bases of ideals in Z[x]
We give an effective procedure to find minimal bases for ideals of the ring of polynomials over the integers.
An elementary proof of the Briançon-Skoda theorem
We give an elementary proof of the Briançon-Skoda theorem. The theorem gives a criterionfor when a function belongs to an ideal of the ring of germs of analytic functions at ; more precisely, the ideal membership is obtained if a function associated with and is locally square integrable. If can be generated by elements,it follows in particular that , where denotes the integral closure of an ideal .
An elementary proof of the Weitzenböck Theorem
An equicharacteristic analogue of Hesselholt's conjecture on cohomology of Witt vectors
Let L/K be a finite Galois extension of complete discrete valued fields of characteristic p. Assume that the induced residue field extension is separable. For an integer n ≥ 0, let denote the ring of Witt vectors of length n with coefficients in . We show that the proabelian group is zero. This is an equicharacteristic analogue of Hesselholt’s conjecture, which was proved before when the discrete valued fields are of mixed characteristic.
An Euler-Poincaré Characteristic for Improper Intersections.
An example concerning the embedded primes associated with an ideal in the ring of polynomials.
An example of a Fréchet algebra which is a principal ideal domain
We construct an example of a Fréchet m-convex algebra which is a principal ideal domain, and has the unit disk as the maximal ideal space.
An example of a simple derivation in two variables
Let k be a field of characteristic zero. We prove that the derivation , where s ≥ 2, 0 ≠ p ∈ k, of the polynomial ring k[x,y] is simple.
An extension of approximation theorems
An extension of Iwasawa's theorem on finitely generated modules over power series rings.
An extension of the Lucas theorem
An extension to fields of positive characteristic of Mather's construction of the Thom-Boardman sequence
An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.
An improvement of Euclid's algorithm
The paper introduces the calculation of a greatest common divisor of two univariate polynomials. Euclid’s algorithm can be easily simulated by the reduction of the Sylvester matrix to an upper triangular form. This is performed by using - transformation and -factorization methods. Both procedures are described and numerically compared. Computations are performed in the floating point environment.
An inequality for Hilbert series of graded algebras.
An iterative construction of bases for finitely generated modules over principal ideal domains
An -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem
Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.
An overview of some recent developments on integer-valued polynomials: Answers and Questions
The purpose of my talk is to give an overview of some more or less recent developments on integer-valued polynomials and, doing so, to emphasize that integer-valued polynomials really occur in different areas: combinatorics, arithmetic, number theory, commutative and non-commutative algebra, topology, ultrametric analysis, and dynamics. I will show that several answers were given to open problems, and I will raise also some new questions.
An upper bound on the number of monomials in determinants of sparse matrices with symbolic entries.
Analytic and Polynominal Homomorphisms of Analytic Rings.