Field Theory (Graduate Texts in Mathematics) - Hardcover

Roman, S.

Hardcover

ISBN 10: 0387944079 ISBN 13: 9780387944074

Publisher: Springer-Verlag New York Inc., 1995

Synopsis

Intended as a course of independent study for graduate students, this text presents the basic theory of fields. It begins with a discussion of polynomials over a ring, the division algorithm, field extensions and embeddings. There is also treatment of Galois theory and binomials.

About this title

Review

From the reviews of the second edition:

"Springer has just released the second edition of Steven Roman’s Field Theory, and it continues to be one of the best graduate-level introductions to the subject out there. ... Every section of the book has a number of good exercises that would make this book excellent to use either as a textbook or to learn the material on your own. All in all, I recommend this book highly as it is a well-written expository account of a very exciting area in mathematics." (Darren Glass, The MAA Mathematical Sciences Digital Library, February, 2006)

“The second edition of Roman’s Field Theory ... offers a graduate course on Galois theory. ... The author’s approach is mainly standard ... . the merits of such an approach would have been helpful for readers who already know some Galois theory, or for instructors who have to pick a textbook. ... The clarity of exposition and lots of exercises make this a suitable textbook for a graduate course on Galois theory.” (Franz Lemmermeyer, Zentralblatt MATH, Vol. 1172, 2009)

From the Back Cover

This book presents the basic theory of fields, starting more or less from the beginning. It is suitable for a graduate course in field theory, or independent study. The reader is expected to have taken an undergraduate course in abstract algebra, not so much for the material it contains but in order to gain a certain level of mathematical maturity.

For this new edition, the author has rewritten the text based on his experiences teaching from the first edition. There are new exercises, a new chapter on Galois theory from an historical perspective, and additional topics sprinkled throughout the text, including a proof of the Fundamental Theorem of Algebra, a discussion of casus irreducibilis, Berlekamp's algorithm for factoring polynomials over Zp and natural and accessory irrationalities.

From the reviews of the first edition:

The book is written in a clear and explanatory style...the book is recommended for a graduate course in field theory as well as for independent study.

- T. Albu, Mathematical Reviews

...[the author] does an excellent job of stressing the key ideas. 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

Edition details

• Publisher: Springer-Verlag New York Inc.
• Publication date: 1995
• Language: English
• ISBN 10: 0387944079
• ISBN 13: 9780387944074
• Binding: Hardcover
• Number of pages: 275