Inequalities for ideal bases in algebraic number fields
نویسندگان
چکیده
منابع مشابه
Gröbner Bases in Orders of Algebraic Number Fields
In the 1960s Bruno Buchberger presented his first critical-pair-completion algorithm, now called Buchberger’s algorithm. Since then Gröbner bases have become a powerful tool in computational algebra and algebraic geometry. What is not as well known is that Buchberger (1985, 1987) has also shown a way of computing Gröbner bases in the integers. This is not as trivial as it may seem. In the polyn...
متن کاملValuation bases for generalized algebraic series fields
a r t i c l e i n f o a b s t r a c t Keywords: Valuation independence Generalized series fields Fields of Puiseux series Restricted exponential function We investigate valued fields which admit a valuation basis. Given a countable ordered abelian group G and a real closed or algebraically closed field F with subfield K , we give a sufficient condition for a valued subfield of the field of gene...
متن کاملAlgebraic number fields
By an algebraic number field we mean a subfield of the algebraic numbers, or an isomorphic copy of such a field. Here we consider questions related to the complexity of determining isomorphism between algebraic number fields. We characterize the algebraic number fields with computable copies. For computable algebraic number fields, we give the complexity of the index sets. We show that the isom...
متن کاملNormal Algebraic Number Fields.
Introduction. In this paper we present a detailed account of the results recently published in the Proceedings of the National Academy of Sciences [29 Our theory is an attempt to generalize the results of the classical class field theory to arbitrary normal fields. In the last analysis, the theory of cyclic extensions Z of an algebraic number field k can be described in terms of cyclic algebras...
متن کاملPrime Number Theorem for Algebraic Function Fields
Elementary proofs of the abstract prime number theorem of the form A(w) = qm + 0(qmm~i) for algebraic function fields are given. The proofs use a refinement of a tauberian theorem of Bombieri. 0. Introduction The main purpose of this paper is to give elementary proofs of the abstract prime number theorem for algebraic function fields (henceforth, the P.N.T.) which was established in the author'...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1964
ISSN: 0004-9735
DOI: 10.1017/s144678870002526x