Results 261 to 270 of about 21,674,610 (304)
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Siberian Mathematical Journal, 2004
Summary: It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal.
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Summary: It is shown that every finite-dimensional skew field whose center is an extremal valued field is defect free. We construct an example of an algebraically complete valued field such that a finite-dimensional skew field over it has a non-trivial defect, that is, there exist algebraically complete valued fields that are not extremal.
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On valuation independence and defectless extensions of valued fields
Journal of Algebra, 2018In this article we further develop the theory of valuation independence and study its relation with classical notions in valuation theory such as immediate and defectless extensions.
Pablo Cubides Kovacsics +2 more
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2017
This chapter introduces the reader to basic field theory by focusing on valued fields. It first considers valuations on fields before discussing the basic properties of valued fields, with emphasis on extensions. It then describes pseudoconvergence in valued fields, along with henselian valued fields.
Matthias Aschenbrenner +2 more
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This chapter introduces the reader to basic field theory by focusing on valued fields. It first considers valuations on fields before discussing the basic properties of valued fields, with emphasis on extensions. It then describes pseudoconvergence in valued fields, along with henselian valued fields.
Matthias Aschenbrenner +2 more
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Russian Mathematical Surveys, 1982
CONTENTS Introduction § 1. Valued fields § 2. Elementary theory of Henselian fields § 3. Multiply valued fields § 4.
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CONTENTS Introduction § 1. Valued fields § 2. Elementary theory of Henselian fields § 3. Multiply valued fields § 4.
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Algebra and Logic, 2007
Summary: We are concerned with a class of valued fields, called stable. We propound an extension of a notion in [\textit{S. Bosch, U. Güntzer}, and \textit{R. Remmert}, Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Berlin: Springer (1984; Zbl 0539.14017)], namely, that of a (ultrametric) norm on groups, rings, algebras ...
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Summary: We are concerned with a class of valued fields, called stable. We propound an extension of a notion in [\textit{S. Bosch, U. Güntzer}, and \textit{R. Remmert}, Non-Archimedean analysis. A systematic approach to rigid analytic geometry, Berlin: Springer (1984; Zbl 0539.14017)], namely, that of a (ultrametric) norm on groups, rings, algebras ...
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2017
This chapter deals with valued differential fields, starting the discussion with an overview of the asymptotic behavior of the function vsubscript P: Γ → Γ for homogeneous P ∈ K K{Y}superscript Not Equal To. The chapter then shows that the derivation of any valued differential field extension of K that is algebraic over K is also small.
Matthias Aschenbrenner +2 more
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This chapter deals with valued differential fields, starting the discussion with an overview of the asymptotic behavior of the function vsubscript P: Γ → Γ for homogeneous P ∈ K K{Y}superscript Not Equal To. The chapter then shows that the derivation of any valued differential field extension of K that is algebraic over K is also small.
Matthias Aschenbrenner +2 more
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Finite Extensions of Valued Fields
Canadian Mathematical Bulletin, 1986AbstractA corollary of the main result is that if L is a finite-dimensional Galois extension of a field K and if w is a valuation of L extending a valuation v of K, then K is closed in L if and only if all valuations of L extending v are dependent. A further consequence is a generalization of Ostrowski's criterion for a real-valued valuation to be ...
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Indexing field values in field oriented systems
Proceedings of the eighth international conference on Information and knowledge management, 1999With the extension of spatial database applications, field oriented systems emerge as an important research issue in order to deal with continuous natural phenomena during the last years. It however has a large volume of data and efficient indexing methods for field data are necessary to overcome the performance obstacle.
Kang, Myoung-Ah +3 more
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2010
Most of the device attribute values could be set by the network manager. Here we list some default values when they are not configured.
Deji Chen, Mark Nixon, Aloysius Mok
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Most of the device attribute values could be set by the network manager. Here we list some default values when they are not configured.
Deji Chen, Mark Nixon, Aloysius Mok
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2016
In the classical settings of the field of complex numbers \( \mathbb{C} \) and the field of real numbers \( \mathbb{R} \), the absolute value plays an important role in the Topology and in the Analysis on objects over these fields. In this chapter, we generalize the absolute value by introducing the notion of valuation on a general field \( \mathbb{K} \
Toka Diagana, François Ramaroson
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In the classical settings of the field of complex numbers \( \mathbb{C} \) and the field of real numbers \( \mathbb{R} \), the absolute value plays an important role in the Topology and in the Analysis on objects over these fields. In this chapter, we generalize the absolute value by introducing the notion of valuation on a general field \( \mathbb{K} \
Toka Diagana, François Ramaroson
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