Chapter II: Field Theory

Emil Artin

Source: Emil Artin, Galois Theory: Lectures Delivered at the University of Notre Dame, ed. and suppl. with a section on applications by Dr. Arthur N. Milgram (Notre Dame, Ind.: University of Notre Dame, 1942), 13-56.

Abstract

Contents

• A. Extension Fields
• B. Polynomials
• C. Algebraic Elements
• D. Splitting Fields
• E. Unique Decomposition of Polynomials into Irreducible Factors
• F. Group Characters
• G. Normal Extensions
• I. Roots of Unity
• J. Noether Equations
• K. Kummer's Fields
• L. Simple Extensions
• M. Existence of a Normal Basis
• N. Theorem of Natural Rationality