منابع مشابه
On integral bases in relative quadratic extensions
Let F be an algebraic number field and E a quadratic extension with E = F(√μ). We describe a minimal set of elements for generating the integral elements oE of E as an oF module. A consequence of this theoretical result is an algorithm for constructing such a set. The construction yields a simple procedure for computing an integral basis of E as well. In the last section, we present examples of...
متن کاملIntegral Function Bases
Integral bases, a minimal set of solutions to Ax ≤ b, x ∈ Zn that generate any other solution to Ax ≤ b, x ∈ Zn, as a nonnegative integer linear combination, are always finite and are at the core of the Integral Basis Method introduced by Haus, Köppe and Weismantel. In this paper we present one generalization of the notion of integral bases to the nonlinear situation with the intention of creat...
متن کاملComputation of integral bases
Let A be a Dedekind domain, K the fraction field of A, and f ∈ A[x] a monic irreducible separable polynomial. For a given non-zero prime ideal p of A we present in this paper a new method to compute a p-integral basis of the extension of K determined by f . Our method is based on the use of simple multipliers that can be constructed with the data that occurs along the flow of the Montes Algorit...
متن کاملHigher Newton Polygons and Integral Bases
Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K at p. The Montes algorithm factorizes a monic irreducible separable polynomial f(x) ∈ A[x] over Kp, and it provides essential arithmetic information about the finite extensions of Kp determined by the different irreducible factors. In particular, it can be us...
متن کاملIntegral bases and p-twisted digraphs
A well-known theorem in network flow theory states that for a strongly connected digraph D = (V, A) there exists a set of directed cycles the incidence vectors of which form a basis for the circulation space of D and integrally span the set of integral circulations; that is, every integral circulation can be written as an integral combination of these vectors. In this paper, we extend this resu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1958
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1958-0093502-7