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