**Course Details:**

Definition of fields, extensions of fields, algebraic extensions, existence of algebraic closure, normal extensions, separable extensions

Galois extensions and Galois theory of finite Galois extensions, solvability by radicals

Definition of modules, finitely generated modules, tensor product of modules, Noetherian rings, Hilbert basis theorem

Modules over a PID, structure theorem for finitely generated abelian groups, Jordan form of matrices over complex numbers**Text Books:**

- Michael Artin, Algebra, Pearson India Education Services Pvt.Ltd. IN Herstein, Topics in algebra, Wiley India Pvt.Ltd.
- Thomas W. Hungerford, Algebra, Graduate Texts in mathematics: 73, Springer-Verlag.
- N. Jacobson, Basic Algebra I, Dover publications

**Reference Books:**

- N. Bourbaki, Algebra I, Springer-Verlag Berlin Heidelberg
- Serge Lang, Algebra, volume 211 of Graduate Texts in Mathematics, Springer-Verlag New York
- Joseph Rotman, Galois theory, Springer-Verlag
- Peter J Cameron, Introduction to Algebra, Oxford University Press