Core Curriculum for Graduate Study Advanced Algebra II (221U4460)
Instructor: Jungkai A. Chen Office: Old Math. Bldg 108 Office Hour: by appointment.
TEL: 23633860-131
Email: jkchen@math.ntu.edu.tw
Fri. @ (12:20-13:10), Sat. 1,2 (8:10-10:00) TA: Huang, Shiu-Lien
TA session: Fri. 4 (11:20-12:10)
First meeting: Feb 20, 2004 ( Fri.)
Course outline:
1. Field Theory
Separable and inseparable extensions.
Transcendental extension and transcendental degree.
2. Ring theory
Modules (homomorphism, tensor product).
Chain conditions.
Jacobson radical.
Density theorem.
Semisimplicity.
3. Commutative algebra (including some algebraic number theory and some algebraic geometry)
Noetherian rings.
Primary decomposition.
Integral extension.
Going-up and going down theorem.
Discrete valuation ring.
Dedekind domain.
Algebraic sets.
Noether normalization theorem and Hibert’s Nullstellensatz.
Dimension theory.
4. Homological algebra
Complexes.
Resolution
Hom, tensor product, Ext and Tor.
Derived category and derived functors.
Reference:
1. Hungerford, Algebra, GTM 73 2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra
5. Eisenbud, Commutative algebra with a view toward algebraic geometry, GTM 150
Grading:
1. Homework 25%
2. Midterm 35%
3. Final Examination 40%
