域和伽罗瓦理论 英文版 Field and Galois Theory/Patrick Morand

Graduate Texts in Mathematics #167

by Patrick Morandi

In the fall of 1990, I taught Math 581 at New Mexico State University for the first time. This course on field theory is the first semester of the year-long graduate algebra course here at NMSU. In the back of my mind, I thought it would be nice someday to write a book on field theory, one of my favorite mathematical subjects, and I wrote a crude form of lecture notes that semester. Those notes sat undisturbed for three years until late in 1993 when I finally made the decision to turn the notes into a book. The notes were greatly expanded and rewritten, and they were in a form sufficient to be used as the text for Math 581 when I taught it again in the fall of 1994. Part of my desire to write a textbook was due to the nonstandard format of our graduate algebra sequence. The first semester of our sequence is field theory. Our graduate students generally pick up group and ring theory in a senior-level course prior to taking field theory. Since we start with field theory, we would have to jump into the middle of most graduate algebra textbooks. This can make reading the text difficult by not knowing what the author did before the field theory chapters. Therefore, a book devoted to field theory is desirable for us as a text. While there are a number of field theory books around, most of these were less complete than I wanted.

Genres: Mathematics, Algebra

Paperback

First published January 1, 1996

Reviews

[George · Rating 5 out of 5]

A crystal clear exposition of Galois theory is presented in the first few chapters. It is so easy to follow that it almost feels like reading a novel at times. The exercises are plentiful and useful. Most of them are relatively easy to check ones' understanding, and a couple are quite challenging. Not much background knowledge other than some linear algebra and basic abstract algebra is required for the first couple of chapters (other than a handful of exercises).

My only gripe is the fact that there are quite a few typos, and although there is a constantly updated errata online, some are still missing. For example, the tower law on finite field extensions is used in an example a few pages before it is even stated (thankfully, I already knew of it before being thoroughly confused). However, this should not be a detriment to anyone that wishes to finally learn Galois theory!

[Jesse · Rating 5 out of 5]

Probably the best book on Galois Theory. Used alongside the relevant chapters from D&F. (Interestingly, the first 2 chapters of this book are explicitly mentioned as the only real prerequisites required for Guillot's book on Class Field Theory).