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 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.
by C. U. Jensen, A. Ledet, N. Yui - Cambridge University Press
A clearly written book, which uses exclusively algebraic language (and no cohomology), and which will be useful for every algebraist or number theorist. It is easily accessible and suitable also for first-year graduate students.
by K.G. Ramanathan - Tata Institute of Fundamental Research
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.
by Emil Artin - University of Notre Dame
The book deals with linear algebra, including fields, vector spaces, homogeneous linear equations, and determinants, extension fields, polynomials, algebraic elements, splitting fields, group characters, normal extensions, roots of unity, and more.