Fields and Galois Theory
نویسنده
چکیده
These notes give a concise exposition of the theory of fields, including the Galois theory of finite and infinite extensions and the theory of transcendental extensions. They are an expansion of those handed out during a course taught to first-year graduate students. v2.01 (August 21, 1996). First version on the web. v2.02 (May 27, 1998). Fixed about 40 minor errors; 57 pages. v3.00 (April 3, 2002). Revised notes; minor additions to text; added 82 exercises with solutions, an examination, and an index; 100 pages. v3.01 (August 31, 2003). Fixed many minor errors; no change to numbering; 99 pages. v4.00 (February 19, 2005). Minor corrections and improvements; added proofs to the section on infinite Galois theory; added material to the section on transcendental extensions; 107 pages. Please send comments and corrections to me at [email protected] Available at http://www.jmilne.org/math/ Copyright c © 1996, 1998, 2002, 2003, 2005. J.S. Milne. This work is licensed under a Creative Commons Licence (Attribution-NonCommercial-NoDerivs 2.0) http://creativecommons.org/licenses/by-nc-nd/2.0/
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