Valuation theory

Otto Endler


  • I Valuations.- x 1 Valuations.- x 2 Completions and extensions of valuations.- x 3 Non-archimedean valuations.- x 4 Discrete exponential valuations.- x 5 Complete discretely valued fields.- II Valuation Rings.- x 6 Valuation rings.- x 7 Krull valuations.- x 8 Places.- x 9 The extension theorem.- x 10 Integrally closed domains 66.- x 11 Prufer rings. Approximation theorems.- x 12 Krull rings and Dedekind rings.- III Extension of Valuation Rings.- x 13 The case of an algebraic field extension.- x 14 The case of a normal field extension.- x 15 Decomposition group and decomposition field.- x 16 Henselian valuation rings.- x 17 Extension of valuation rings and henselization.- x 18 The equality ? ei * fi = n.- x 19 Inertia group and inertia field.- x 20 Ramification group and ramification field.- x 21 Higher ramification groups.- x 22 Unramified and tamely ramified extensions.- IV Fields with Prescribed Valuations.- x 23 Introduction and notation.- x 24 Topological preliminaries.- x 25 Solvable (?1,...,?k)-prescriptions.- x 26 Henselian and antihenselian valuations.- x 27 Prescription of value groups and residue fields.- x 28 The case of infinite field extensions.- Exercises.

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書名 Valuation theory
著作者等 Endler, Otto
シリーズ名 Universitext
出版元 Springer-Verlag
刊行年月 1972
版表示 Softcover reprint of the original 1st ed. 1972
ページ数 xii, 243 p.
大きさ 26 cm
ISBN 3540060707
NCID BA00655058
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言語 英語
出版国 ドイツ