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Fields and Galois Theory

Fields and Galois MilneQ Q Cx Q p 7 Qh 3ih 2ih i=h 3ih i=h 2iSplitting field ofX7 ; Q Q QNHG=NSplitting field ofX5 2018 These notes give a concise exposition of the Theory of Fields , including the Galois theoryof finite and infinite extensions and the Theory of transcendental extensions. The first sixchapters form a standard course, and the final three chapters are more information@misc{milneFT,author={Milne, James S.},title={ Fields and Galois Theory ( )},year={2018},note={Available at },pages={138}} (August 21, 1996). First version on the (May 27, 1998). Fixed many minor errors; 57 (April 3, 2002). Revised notes; minor additions to text; added 82 exercises withsolutions, an examination, and an index; 100 (August 31, 2003). Fixed many minor errors; numbering unchanged; 99 (February 19, 2005).

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.

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