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.

    1: Finite Cogalois Theory; 1: Preliminaries; 2: Kneser Extensions; 3: Cogalois Extensions; 4: Strongly Kneser Extensions; 5: Galois G-Cogalois Extensions; 6: Radical Extensions and Crossed Homomorphisms; 7: Examples of G-Cogalois Extensions; 8: G-Cogalois Extensions and Primitive Elements; 9: Applications to Algebraic Number Fields; 10: Connections with Graded Algebras and Hopf Algebras; 2: Infinite Cogalois Theory; 11: Infinite Kneser Extensions; 12: Infinite G -Cogalois Extensions; 13: Infinite Kummer Theory; 14: Infinite Galois Theory and Pontryagin Duality; 15: Infinite Galois G-Cogalois Extensions


    Toma Albu

    "The author is an important contributor to the subject, and the volume contains many of his results. The book is carefully written … Over 250 exercises, an up-to-date bibliography and an extensive index add to the value of the book. This volume is especially recommended to students and researchers in Algebraic Number Theory, but any algebraist will find here interesting ideas and information."
    - Studia Universitatis Babes-Bolyai Series Mathematica, Vol. XLVIII, No. 4, 2003

    "The book is rich in many examples and exercises."
    -Zentralblatt MATH

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