منابع مشابه
Infinite Hilbert Class Field Towers over Cyclotomic Fields
Weuse a result of Y. Furuta to show that for almost all positive integers m, the cyclotomic field (exp(2π i/m)) has an infinite Hilbert p-class field tower with high rankGalois groups at each step, simultaneously for all primes p of size up to about (log logm)1+o(1). We also use a recent result of B. Schmidt to show that for infinitely many m there is an infinite Hilbert p-class field tower ove...
متن کاملOn 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 کاملA Relative Integral Basis over Q( √−3) for the Normal Closure of a Pure Cubic Field
Let K be a pure cubic field. Let L be the normal closure of K. A relative integral basis (RIB) for L over Q(√ −3) is given. This RIB simplifies and completes the one given by Haghighi (1986).
متن کاملOn Gröbner bases and Krull dimension of residue class rings of polynomial rings over integral domains
Given an ideal a in A[x1, . . . , xn] where A is a Noetherian integral domain, we propose an approach to compute the Krull dimension of A[x1, . . . , xn]/a, when the residue class ring is a free A-module. When A is a field, the Krull dimension of A[x1, . . . , xn]/a has several equivalent algorithmic definitions by which it can be computed. But this is not true in the case of arbitrary Noetheri...
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In our recent paper I. Gaál: Calculating “small” solutions of relative Thue equations, J. Experiment. Math. (to appear) we gave an efficient algorithm to calculate “small” solutions of relative Thue equations (where “small” means an upper bound of type 10500 for the sizes of solutions). Here we apply this algorithm to calculating power integral bases in sextic fields with an imaginary quadratic...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2002
ISSN: 0022-314X
DOI: 10.1016/s0022-314x(02)00009-4