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, 2nd ed. (Notre Dame, Ind.: University of Notre Dame, 1971), 21-68.

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. Applications and Examples to Theorem 13
• H. Normal Extensions
• I. Finite Fields
• J. Roots of Unity
• K. Noether Equations
• L. Kummer's Fields
• M. Simple Extensions
• N. Existence of a Normal Basis
• O. Theorem of Natural Rationality