Cogalois theory
著者
書誌事項
Cogalois theory
（Monographs and textbooks in pure and applied mathematics, v. 252）
Marcel Dekker, c2003
- : hbk
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注記
Bibliography: p. 329-333
Includes index
内容説明・目次
内容説明
This volume offers a systematic, comprehensive investigation of field extensions, finite or not, that possess a Cogalois correspondence. The subject is somewhat dual to the very classical Galois Theory dealing with field extensions possessing a Galois correspondence. Solidly backed by over 250 exercises and an extensive bibliography, this book presents a compact and complete review of basic field theory, considers the Vahlen-Capelli Criterion, investigates the radical, Kneser, strongly Kneser, Cogalois, and G-Cogalois extensions, discusses field extensions that are simultaneously Galois and G-Cogalois, and presents nice applications to elementary field arithmetic.
目次
- Finite Cogalois theory: preliminaries
- Kneser extensions
- Cogalois extensions
- strong Kneser extensions
- Galois G-Cogalois extensions
- radical extensions and crossed homomorphisms
- examples of G-Cogalois extensions
- G-Cogalois extensions andprimitive elements
- applications to algebraic number fields
- connections with graded algebras and Hopf algebras. Infinite Cogalois Theory: infinite Kneser extensions
- infinite G-Cogalois extensions
- infinite Kummer theory
- infinite Galois theory andPontryagin duality
- infinite Galois G-Cogalois extensions.
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