AbstractThe theory of valuations on fields is developed in the constructive spirit of Errett Bishop. As a consequence of the general theory we are able to construct all nonarchimedean valuations on algebraic number fields and compute their ramification indices and residue class degrees. The notion of a field with a valuation for which the infimum of the values of any polynomial function can be computed plays an important role. Numerous limiting counterexamples are provided
This article is in the nature of a survey of the theory of complete fields. It is not exhaustive but...
AbstractThe classical theory of Gröbner bases, as developed by Bruno Buchberger, can be expanded to ...
AbstractIf a valuation ring V on a simple transcendental field extension K0(X) is such that the resi...
AbstractThe theory of valuations on fields is developed in the constructive spirit of Errett Bishop....
This thesis investigates some properties of valuations on fields. Basic definitions and theorems as...
This monograph is the first book-length treatment of valuation theory on finite-dimensional division...
Absolute values and their completions - like the p-adic number fields- play an important role in num...
Classical valuation theory has applications in number theory and class field theory as well as in al...
Classical valuation theory has applications in number theory and class field theory as well as in al...
If R is a field on which all (non-archimedean) valuations are known, then all valuations on R[x], wh...
If R is a field on which all (non-archimedean) valuations are known, then all valuations on R[x], wh...
The book deals with the (elementary and introductory) theory of valuation rings. As explained in the...
82 pagesThe purpose of this paper is to extend some results from the theory of valuations on a fiel...
We explain how to compute in the algebraic closure of a valued field. These computa-tions heavily re...
This thesis assembles some new results in the field arithmetic of various classes of fields, includi...
This article is in the nature of a survey of the theory of complete fields. It is not exhaustive but...
AbstractThe classical theory of Gröbner bases, as developed by Bruno Buchberger, can be expanded to ...
AbstractIf a valuation ring V on a simple transcendental field extension K0(X) is such that the resi...
AbstractThe theory of valuations on fields is developed in the constructive spirit of Errett Bishop....
This thesis investigates some properties of valuations on fields. Basic definitions and theorems as...
This monograph is the first book-length treatment of valuation theory on finite-dimensional division...
Absolute values and their completions - like the p-adic number fields- play an important role in num...
Classical valuation theory has applications in number theory and class field theory as well as in al...
Classical valuation theory has applications in number theory and class field theory as well as in al...
If R is a field on which all (non-archimedean) valuations are known, then all valuations on R[x], wh...
If R is a field on which all (non-archimedean) valuations are known, then all valuations on R[x], wh...
The book deals with the (elementary and introductory) theory of valuation rings. As explained in the...
82 pagesThe purpose of this paper is to extend some results from the theory of valuations on a fiel...
We explain how to compute in the algebraic closure of a valued field. These computa-tions heavily re...
This thesis assembles some new results in the field arithmetic of various classes of fields, includi...
This article is in the nature of a survey of the theory of complete fields. It is not exhaustive but...
AbstractThe classical theory of Gröbner bases, as developed by Bruno Buchberger, can be expanded to ...
AbstractIf a valuation ring V on a simple transcendental field extension K0(X) is such that the resi...
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