contents - 38 H Normal Extensions 41 I Finite Fields 49 J...

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TABLE OF CONTENTS (The sections marked with an asterisk have been herein added to the content of the first edition) Page I LINEAR ALGEBRA 1 A. Fields 1 B. Vector Spaces 1 C. Homogeneous Linear Equations 2 D. Dependence and Independence of Vectors 4 E. Non-homogeneous Linear Equations 9 F.* Determinants 11 II FIELD THEORY 21 A. Extension Fields 21 B. Polynomials 22 C. Algebraic Elements 25 D. Splitting Fields 30 E. Unique Decomposition of Polynomials into Irreducible Factors 33 F. Group Characters 34 G.* Applications and Examples to Theorem 13
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Unformatted text preview: 38 H. Normal Extensions 41 I. Finite Fields 49 J. Roots of Unity 56 K. Noether Equations 57 L. Rummer's Fields 59 M. Simple Extensions 64 N. Existence of a Normal Basis 66 O. Theorem on Natural Irrationalities 67 III APPLICATIONS By A. N. Milgram 69 A. Solvable Groups 69 B. Permutation Groups 70 C. Solution of Equations by Radicals 72 D. The General Equation of Degree n 74 E. Solvable Equations of Prime Degree 76 F. Ruler and Compass Construction 80...
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This note was uploaded on 11/14/2011 for the course MATH 367 taught by Professor Sdd during the Spring '11 term at Middle East Technical University.

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