Field Theory

Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings. The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. The book concludes with a chapter on families of binomials a? the Kummer theory. This new edition has been completely rewritten in order to improve the pedagogy and to make the text more accessible to graduate students. The exercises have also been improved and a new chapter on ordered fields has been included. About the first edition: " ...the author has gotten across many important ideas and results. This book should not only work well as a textbook for a beginning graduate course in field theory, but also for a student who wishes to take a field theory course as independent study." -J.N. Mordeson, Zentralblatt "The book is written in a clear and explanatory style. It contains over 235 exercises which provide a challenge to the reader. The book is recommended for a graduate course in field theory as well as for independent study." - T. Albu, MathSciNetRoman, Steven is the author of 'Field Theory ', published 2005 under ISBN 9780387276779 and ISBN 0387276777.