منابع مشابه
Witt rings of quadratically presentable fields
This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability. It turns out that the classical notion of the Witt ring of symmetric bilinear forms over a field makes sense in the context of {tmem{quadratically p...
متن کاملWitt Equivalence of Function Fields over Global Fields
Witt equivalent fields can be understood to be fields having the same symmetric bilinear form theory. Witt equivalence of finite fields, local fields and global fields is well understood. Witt equivalence of function fields of curves defined over archimedean local fields is also well understood. In the present paper, Witt equivalence of general function fields over global fields is studied. It ...
متن کاملCharacterizing Reduced Witt Rings of Fields
Let IV(F) denote the Mitt ring of nondegenerate symmetric bilinear forms over a field F. In this paper wc shall be concerned only with formally real fields, for which we write Wr,,l(F) ~mm W(F)/Wil W(F) for the reduced R’itt ring. In [13, 141 the rings W(F) and iTred are shown to be special cases of absfrart lWtt rirqs and a great deal of the ring structure is developed in this setting. In [6] ...
متن کاملWitt Rings and Matroids
The study of Witt rings of formally real fields in the algebraic theory of quadratic forms has led to a particularly good understanding of the finitely generated torsion free Witt rings. In this paper, we work primarily with a somewhat more general class of rings which can be completely characterized by (binary) matroids. The different types of standard constructions and invariants coming from ...
متن کاملHolomorphy rings of function fields
In his 1974 text, Commutative Ring Theory, Kaplansky states that among the examples of non-Dedekind Prüfer domains, the main ones are valuation domains, the ring of entire functions and the integral closure of a Prüfer domain in an algebraic extension of its quotient field [Kap74, p.72]. A similar list today would likely include Kronecker function rings, the ring of integervalued polynomials an...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2000
ISSN: 0208-6573
DOI: 10.7169/facm/1538186701