Search results for: Ilaria Del Corso

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Finite groups of units of finite characteristic rings

Ilaria Del Corso, Roberto Dvornicich

Annali di Matematica Pura ed Applicata ( 01923 -) > 2018 > 197 > 3 > 661-671

Fuchs (Abelian groups, Pergamon, Oxford, 1960, Problem 72) asked the following question: which groups can be the group of units of a commutative ring? In the following years, some partial answers have been given to this question in particular cases. The aim of the present paper is to address Fuchs’ question when A is a finite characteristic ring. The result is a pretty good description of the groups...

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On wild extensions of a p-adic field

Ilaria Del Corso, Roberto Dvornicich, Maurizio Monge

Journal of Number Theory > 2017 > 174 > C > 322-342

In this paper we consider the problem of classifying the isomorphism classes of extensions of degree pk of a p-adic field K, restricting to the case of extensions without intermediate fields.We establish a correspondence between the isomorphism classes of these extensions and some Kummer extensions of a suitable field F containing K. We then describe such classes in terms of the representations of...

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Normal integral bases and tameness conditions for Kummer extensions

Ilaria Del Corso, Lorenzo Rossi

Acta Arithmetica > 2013 > 160 > 1 > 1-23

We present a detailed analysis of some properties of a general tamely ramified Kummer extension of number fields L/K. Our main achievement is a criterion for the existence of a normal integral basis for a general Kummer extension, which generalizes the existing results. Our approach also allows us to explicitly describe the Steinitz class of L/K and we get an easy criterion for this class to be trivial...

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Normal integral bases for cyclic Kummer extensions

Ilaria Del Corso, Lorenzo Paolo Rossi

Journal of Pure and Applied Algebra > 2010 > 214 > 4 > 385-391

Let K/F be a Kummer cyclic extension of number fields. In the case when the degree is a prime number, Gómez Ayala gave an explicit criterion for the existence of a normal integral basis. More recently Ichimura proposed a generalization of that result for cyclic extensions of arbitrary degree, but we have found that Ichimura’s result is incorrect. In this paper we present a counter-example to Ichimura’s...

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The Compositum of Wild Extensions of Local Fields of Prime Degree

Ilaria Del Corso, Roberto Dvornicich

Monatshefte für Mathematik > 2007 > 150 > 4 > 271-288

. In this paper we present a general view of the totally and wildly ramified extensions of degree p of a p-adic field K. Our method consists in deducing the properties of the set of all extensions of degree p of K from the study of the compositum ${\cal C}_K(p)$ of all its elements. We show that in fact ${\cal C}_K(p)$ is the maximal abelian extension of exponent p of F = F(K), where F is...

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An equivalence between local fields

Ilaria Del Corso, Roberto Dvornicich

Journal of Number Theory > 2005 > 115 > 2 > 230-248

The p-component of the index of a number field K depends only on the completions of K at the primes over p. In this paper we define an equivalence relation between m-tuples of local fields such that, if two number fields K and K′ have equivalent m-tuples of completions at the primes over p, then they have the same p-component of the index. This equivalence can be interpreted in terms of the decomposition...

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Decomposition of primes in non-maximal orders

Ilaria Del Corso, Roberto Dvornicich, Denis Simon

Acta Arithmetica > 2005 > 120 > 3 > 231-244

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Relations among Discriminant, Different, and Conductor of an Order

Ilaria Del Corso, Roberto Dvornicich

Journal of Algebra > 2000 > 224 > 1 > 77-90

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Uniformity over primes of tamely ramified splittings

Ilaria Del Corso, Roberto Dvornicich

manuscripta mathematica > 2000 > 101 > 2 > 239-266

Abstract:We fix a prime p and let f(X) vary over all monic integer polynomials of fixed degree n. Given any possible shape of a tamely ramified splitting of p in an extension of degree n, we prove that there exists a rational function (X)(X) such that the density of the monic integer polynomials f(X) for which the splitting of p has the given shape in [X]/f(X) is (p) (here reducible polynomials can...

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Factorization of Prime Ideal Extensions in Dedekind Domains

Ilaria del Corso

Journal of Symbolic Computation > 1995 > 19 > 5 > 435-439

In this paper, improving on the results of Del Corso (1992), we describe a method to factorize prime ideal extensions in Dedekind domains. This method needs factorization modulo P of a polynomial in at least two variables.

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