Course Content: 

 

  1. Definition of field, extensions of fields, algebraic extensions, existence of algebraic closure, normal extensions, separable extensions (11 Lectures)
  2. Galois extensions and Galois theory of finite Galois extensions (10 Lectures)
  3. Modules,  Noetherian rings, Hilbert basis theorem (15 Lectures)
  4. Structure theorem for finitely generated modules over PID (6 Lectures)

Learning Outcomes: upon successful completion of the course,

 1. the students will have a good understanding of the theory of Fields and modules

 2. they will be able to appreciate the power of abstraction and gain mathematical maturity.

 

Text/Reference Books:

1. Michael Artin, Algebra, Pearson India Education Services Pvt.Ltd, ISBN: 978-93-325-4983-8

2. IN Herstein, Topics in Algebra, Wiley India Pvt.Ltd, ISBN: 978-81-265-1018-4

3. Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics: 73, Springer-Verlag,

     ISBN:978-0-387-90518-1, ISBN: 978-1-4612-6103-2

4. N. Jacobson, Basic Algebra I, Dover publications, ISBN-10: 9780486471891

5. David S. Dummit, Richard M. Foote: Abstract Algebra, second edition, John Wiley and Sons,

    Inc., ISBN-13: ‎ 978-0471368571