𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Factorization of Prime Ideal Extensions in Dedekind Domains

✍ Scribed by Ilaria del Corso


Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
136 KB
Volume
19
Category
Article
ISSN
0747-7171

No coin nor oath required. For personal study only.

✦ Synopsis


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.


πŸ“œ SIMILAR VOLUMES


The Least Nonsplit Prime in Galois Exten
✍ Jeffrey D Vaaler; JosΓ© Felipe Voloch πŸ“‚ Article πŸ“… 2000 πŸ› Elsevier Science 🌐 English βš– 141 KB

Let k be a Galois extension of Q with [k : Q]=d 2. The purpose of this paper is to give an upper bound for the least prime which does not split completely in k in terms of the degree d and the discriminant 2 k . Our estimate improves on the bound given by Lagarias et al. [3]. We note, however, that

On the Parity of Exponents in the Prime
✍ J.W. Sander πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 126 KB

In 1997 Berend proved a conjecture of Erdo s and Graham by showing that for every positive integer r there are infinitely many positive integers n with the property that where p(1)=2, p(2)=3, p(3)=5, ... is the sequence of primes in ascending order, and e p (m) denotes the order of the prime p in t

Extension of Ideal-Theoretic Properties
✍ H.Pat Goeters; Bruce Olberding πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 127 KB

We examine when multiplicative properties of ideals extend to submodules of the quotient field of an integral domain. An integral domain R is stable if each non-zero ideal of R is invertible as an ideal over its ring of endomorphisms. We show that an integral domain R is stable if and only if an ana

On Capitulation of S-Ideals in Zp-Extens
✍ Hiroki Sumida πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 167 KB

Let k be a finite extension of Q and p a prime number. Let K be a Z p -extension of k and S the set of all prime ideals in k which are ramified in K. We denote by A$ the p-Sylow subgroup of the S-divisor class group of K. We give a criterion for A$ =0 which can be applied for general Z p -extensions