HNGU M.SC. MATHEMATICS SEMESTER - 4
MSM1402 β FILED THEORY
Unit 1:
- Extensions of field
- Finite extension
- Algebraic field extension
- Simple field extensions
- Transcendental numbers
Unit 2:
- Roots of polynomials
- The splitting field of a polynomial over a field
- Construction with straightedge and compass
Unit 3:
- The fixed field of a group of automophisms
- The theorem on symmetric polynomials
- Normal field extension
- The Galois group of a polynomial
Unit 4:
- The fundamental theorem of Galois theory
- Solvability by radicals
- Galois group over the Rationals
- Finite fields
Note: The topics are covered by chapter 5 (all articles) and chapter 7 (7.1 and 7.2 only) of the book, Topics in Algebra - I. N. Herstein 2nd Edition, Wiley Eastern Ltd., 1975.
1. Basic Algebra - Jacobson Vol. I & II Hindustan Publishing Co., 1984.
2. Basic Abstract Algebra - P B Bhattacharya, S K Jain, S R Nagpaul, 2nd Edition, Cambridge University Press, 1995.
3. Algebra - Lang S, Addison β Wesley, Reading, Mass, 1965.
4. Algebra - Artin M, Prentice Hall, Englewood Cliffs N J, 1991.
5. Abstract Algebra - David S. Dummit and Richard M β Foote, Prentice Hall, Englewood.
6. University Algebra - Vijay Krishnan.
7. A first course in Abstract Algebra - John Fraleigh, Nawsa Publishing 3rd Edition House.
8. A textbook of Modern Abstract Algebra - Shanti Narayan & Satpal, S. Chane & Company.
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