Algebra13

MTH620 - Algebra II (Graduate Course)

Instructor : Dr. Anupam Singh

Schedule : Wednesday 10-11:30 and Thursday 2:30-4 in Ramanujan Hall

Evaluation : four tests including mid-sem and end-sem

Topics :

• Bilinear Forms, Classical Groups.

• Field Theory: Separable and Normal extensions, Finite Fields, Algebraic and Transcendental extensions, Galois’ theorem, Infinite Galois Groups, Hilbert 90.

• Commutative Algebra: Localization, DVR, Noetherian, Hilbert Basis Theorem, Dedekind domains, Integral extensions, Hilbert's Nullstellensatz, spec of a ring.

• Homological Algebra: Projective and Injective Modules, Ext and Tor functors, connecting homomorphism.

References :

• • Classical Groups and Geometric Algebra : Grove

  • Abstract Algebra : Dummit and Foote

  • Algebra : Lang

  • Introduction to Commutative Algebra : Atiyah and Macdonald

  • Steps in Commutative Algebra : Sharp