Grad Algebra II
Textbook: None.  
Course Notes  Date  Details 

Homework 1 Solutions  Tues, Feb 4 
Course Notes Abstract Galois Connections Field of Fractions Localization C(X) for Compact, Hausdorff X Weak Nullstellensatz for C(X) Localization = Germs of Functions 
Homework 2 Solutions  Tues, Feb 25 
Course Notes What do Z and K[x] have in common? Euclidean => PID => UFD Noetherian Rings Who cares about unique factorization? Riemann Surfaces vs. Algebraic Integers 
Homework 3 Solutions  Thurs, Mar 20 
Gauss' Lemma (R UFD implies R[y] UFD) Z[y] and K[x,y] are UFDs, but they are not PIDs. Nonmaximal primes in Z[y] and K[x,y] 
Homework 4 Solutions  Thurs , Apr 17 
Course Notes Ring Extensions and Evaluation Morphisms KAlgebras vs. KModules F.G. & Algebraic => Field (not hard) F.G. & Field => Algebraic (hard) K[x1,..,xn] is a UFD (Gauss' Lemma) K[x1,..,xn] is Noetherian (Hilbert's Basis Theorem) Weak Nullstellensatz 
No HW5 
Course Notes Variety = Radical Ideal (Strong NSS) Irreducible Variety = Prime Ideal Krull Dimension Algebraic Independence Transcendence Degree Noether Normalization Zariski's Lemma Proof of the NSS Epilogue: dim(V) = tr.deg(K[V]) 

Final Exam Solutions 
Thurs, May 1  
Algebra Qual 
Fri, June 6 
Review Session 1 Review Session 2 Review Session 3 Review Session 4 