The embedding problem in Galois theory
Author(s)
Bibliographic Information
The embedding problem in Galois theory
（Translations of mathematical monographs, v. 165）
American Mathematical Society, c1997
- : hc
- Other Title
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Задача погружения в теории Галуа
Zadacha pogruzhenii︠a︡ v teorii Galua
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
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Note
Bibliography: p. 175-179
Includes index
Description and Table of Contents
Description
The central problem of modern Galois theory involves the inverse problem: given a field $k$ and a group $G$, construct an extension $L/k$ with Galois group $G$. The embedding problem for fields generalizes the inverse problem and consists in finding the conditions under which one can construct a field $L$ normal over $k$, with group $G$, such that $L$ extends a given normal extension $K/k$ with Galois group $G/A$. Moreover, the requirements applied to the object $L$ to be found are usually weakened: it is not necessary for $L$ to be a field, but $L$ must be a Galois algebra over the field $k$, with group $G$.In this setting, the embedding problem is rich in content. But the inverse problem in terms of Galois algebras is poor in content because a Galois algebra providing a solution of the inverse problem always exists and may be easily constructed. The embedding problem is a fruitful approach to the solution of the inverse problem in Galois theory. This book is based on D. K. Faddeev's lectures on embedding theory at St. Petersburg University and contains the main results on the embedding problem. All stages of development are presented in a methodical and unified manner.
Table of Contents
Preliminary information about the embedding problem The compatibility condition the embedding problem with Abelian kernel The embedding problem for local fields the embedding problem with non-Abelian kernel for algebraic number fields Appendix Bibliography Subject index.
by "Nielsen BookData"
