The Elements of the Theory of Algebraic Numbers
by Legh Wilber Reid
Publisher: The Macmillan company 1910
Number of pages: 488
It has been my endeavor in this book to lead by easy stages a reader, entirely unacquainted with the subject, to an appreciation of some of the fundamental conceptions in the general theory of algebraic numbers. With this object in view, I have treated the theory of rational integers more in the manner of the general theory than is usual, and have emphasized those properties of these integers which find their analogues in the general theory.
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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.
by Mark Reeder - Boston College
From the table of contents: Basic ring theory, polynomial rings; Finite fields; Extensions of rings and fields; Computing Galois groups of polynomials; Galois groups and prime ideals; Cyclotomic extensions and abelian numbers.
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The text demonstrates the use of general concepts by applying theorems from various areas in the context of one problem -- solving the quintic. This book helps students to develop connections between the algebra, geometry, and analysis ...
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These lecture notes on Field theory are aimed at providing the beginner with an introduction to algebraic extensions, algebraic function fields, formally real fields and valuated fields. We assume a familiarity with group theory and vector spaces.