Course Content:
- Definition of field, extensions of fields, algebraic extensions, existence of algebraic closure, normal extensions, separable extensions (11 Lectures)
- Galois extensions and Galois theory of finite Galois extensions (10 Lectures)
- Modules, Noetherian rings, Hilbert basis theorem (15 Lectures)
- 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