Galois Theory: Lectures Delivered at the University of Notre Dame
by Emil Artin
Publisher: University of Notre Dame 1971
Number of pages: 96
The first section deals with linear algebra, including fields, vector spaces, homogeneous linear equations, determinants, and other topics. A second section considers extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, Noether equations, Jummer's fields, and more.
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by J. S. Milne
Class field theory describes the abelian extensions of a local or global field in terms of the arithmetic of the field itself. These notes contain an exposition of abelian class field theory using the algebraic/cohomological approach.
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The author discusses the problem of solutions of polynomial equations both in explicit terms and in terms of abstract algebraic structures. The course demonstrates the tools of abstract algebra as applied to a meaningful problem.
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A concise treatment of Galois theory and the theory of fields, including transcendence degrees and infinite Galois extensions. Contents: Basic definitions and results; Splitting fields; The fundamental theorem of Galois theory; etc.
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