An addendum to the paper: “Arithmetic functions over rings with zero divisors” by Ruangsinsap, Laohakosol and P. Udomkavanich.
An algorithm for primary decomposition in polynomial rings over the integers
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals, resp. over finite fields, and the idea of Shimoyama-Yokoyama, resp. Eisenbud-Hunecke-Vasconcelos, to extract primary ideals from pseudo-primary ideals. A parallelized version of the algorithm is implemented in Singular. Examples and timings are given at the end of the article.
An Arithmetic Characterization of the Rational Homotopy Groups of Certain Spaces.
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 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 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 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 inequality for Hilbert series of graded algebras.
An iterative construction of bases for finitely generated modules over principal ideal domains
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.
Anelli di frazioni fortemente valutativi
Anelli -adici e loro rappresentazioni
Anneaux de Fatou
Anneaux de 'polynômes à valeurs entières' et anneaux de Fatou
Anneaux de polynômes à valeurs entières sur un anneau de valuation ou de Seidenberg
Anneaux de polynômes sur un anneau de Mori