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Reverse Mathematics and Algebraic Field Extensions [PDF]
Computability, 2013 This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section §2, we show that WKL0 is equivalent to the ability to extend F-automorphisms of field extensions to automorphisms of $\bar F$, the algebraic closure of F. Section §3 explores finitary conditions for embeddability.
Paul Shafer +2 more
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Valuations in algebraic field extensions
Journal of Algebra, 2007 Let $K\to L$ be an algebraic field extension and $ν$ a valuation of $K$. The purpose of this paper is to describe the totality of extensions $\left\{ν'\right\}$ of $ν$ to $L$ using a refined version of MacLane's key polynomials. In the basic case when $L$ is a finite separable extension and $rk ν=1$, we give an explicit description of the limit key ...
Mark Spivakovsky
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Fuzzy algebraic field extensions
Fuzzy Sets and Systems, 1992The concept of fuzzy algebraic field extensions is introduced. Conditions are determined for which a fuzzy algebraic field extension has unique maximal fuzzy intermediate fields which are fuzzy separable algebraic and fuzzy purely inseparable. The fuzzification of other basic properties of field extensions is examined.
John Mordeson
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2017
Recall that a field extension \(\mathbb{k} \subset \mathbb{F}\) is said to be finite of degree d if \(\mathbb{F}\) has dimension d < ∞ as a vector space over \(\mathbb{k}\). We write \(\deg \mathbb{F}/\mathbb{k} = d\) in this case.
Alexey L Gorodentsev +1 more
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Recall that a field extension \(\mathbb{k} \subset \mathbb{F}\) is said to be finite of degree d if \(\mathbb{F}\) has dimension d < ∞ as a vector space over \(\mathbb{k}\). We write \(\deg \mathbb{F}/\mathbb{k} = d\) in this case.
Alexey L Gorodentsev +1 more
exaly +2 more sources
A treatise on field extensions and algebraic extensions
AIP Conference ProceedingsMahaboob B, B Mahaboob, Y Hari Krishna
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Parametrization of Algebraic Curves over Optimal Field Extensions
Journal of Symbolic Computation, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Franz Winkler
exaly +3 more sources