Math 742 - Abstract Algebra II (Spring 2016)

Past algebra qualifying exams




This will be adjusted as necessary.
Jan 20AK 1-3: Rings, prime ideals, radical ideals
Jan 22AK 4: Modules
Jan 25AK 5: Exact sequences
Jan 27AK 6: Direct limits
Jan 29AK 7: Filtered direct limits
Feb 1AK 8: Tensor products
Feb 3AK 9: Flatness
Feb 5AK 10: Cayley-Hamilton theorem
Feb 8Finish AK 10
Feb 10AK 11: Localization of rings
Feb 12AK 12: Localization of modules
Feb 15AK 14: Krull-Cohen-Seidenberg theory
Feb 17AK 15: Noether normalization
Feb 19Finish AK 15
Feb 22AK 16: Chain conditions
Feb 24AK 17: Associated primes
Feb 26AK 18: Primary decomposition
Feb 29Finish AK 18
Mar 2AK 19: Length
Mar 4Finish AK 19
Mar 7AK 20: Hilbert functions
Mar 9Finish AK 20
Mar 11AK 21: Dimension
Mar 14Lang V.1-V.2: Finite and algebraic extensions; algebraic closure
Mar 16Lang V.3: Splitting fields and normal extensions
Mar 18Lang V.4: Separable extensions
Spring break
Mar 28Finish V.4
Mar 30Lang V.5: Finite fields
Apr 1Lang VI.1: Galois extensions
Apr 4Finish VI.1
Apr 6Lang VI.2: Examples
Apr 8Lang VI.3: Roots of unity
Apr 11Lang V.6: Inseparable extensions; VI.4: Linear independence of characters
Apr 13Lang VI.5: Norm and trace
Apr 15Finish VI.5; Lang VI.6: Cyclic extensions
Apr 18Lang VI.7: Solvable and radical extensions
Apr 20Finish VI.7
Apr 22Lang XV.8: Alternating forms
Apr 25Lang XV.9: Pfaffians
Apr 27Lang XIX.1: Exterior algebras
Apr 29Finish XIX.1
May 2Inverse limits; Lang Exercise VI.43: Profinite topology
May 4Lang VI.14: Infinite Galois extensions
May 6Next steps: overview of more advanced algebraic topics