Notre Dame Mathematical Lectures

Chapter II: Field Theory

Arthur N. Milgram

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  • 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

Chapter information

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

First available in Project Euclid: 29 March 2007

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Copyright © 1971, University of Notre Dame


Artin, Emil. Chapter II: Field Theory. Galois Theory, 21--68, University of Notre Dame, Notre Dame, Indiana, 1971.

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