Fields and Galois Theory
by J. S. Milne
Number of pages: 111
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; multiple roots. The fundamental theorem of Galois theory. Computing Galois groups. Applications of Galois theory. Algebraic closures. Infinite Galois theory. Transcendental Extensions.
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by Sudhir R. Ghorpade - Indian Institute of Technology, Bombay
These are notes of a series of lectures, aimed at covering the essentials of Field Theory and Ramification Theory as may be needed for local and global class field theory. Included are the two sections on cyclic extensions and abelian extensions.
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.
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 M. Kneser - Tata Institute of Fundamental Research
The main result is the Hasse principle for the one-dimensional Galois cohomology of simply connected classical groups over number fields. For most groups, this result is closely related to other types of Hasse principle.