Lectures on the Algebraic Theory of Fields

Small book cover: Lectures on the Algebraic Theory of Fields

Lectures on the Algebraic Theory of Fields

Publisher: Tata Institute of Fundamental Research
Number of pages: 228

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, vector spaces and ideal theory of rings.

Download or read it online for free here:
Download link
(930KB, PDF)

Similar books

Book cover: Class Field TheoryClass Field Theory
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.
Book cover: Galois Theory: Lectures Delivered at the University of Notre DameGalois Theory: Lectures Delivered at the University of Notre Dame
by - 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.
Book cover: Notes on Galois TheoryNotes on Galois Theory
by - 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.
Book cover: Galois TheoryGalois Theory
by - University of Warwick
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.