Advanced Algebra II, Spring 2004

¡@ meeting time meeting place
classes: Fri. 12:20-13:10 Old Math 103
¡@ Sat. 8:10-10:00 New Math 102
TA session: Fri. 13:20-14:10 Old Math 103

NB: most documents are in pdf format. You might need Acrobat Reader (which is free to download) to view it. Some version of Ghostview also works.

syllabus

Final Examination: Due on Jun 18. 2004.

Lecture Notes:

lecture 1:  Separability and inseparability

lecture 2:  Transcendental extension

lecture 3: Modules

lecture 4: Free modules, modules over principal ideal domain I.

lecture 5: Modules over principal ideal domain II.

lecture 6: Modules over principal ideal domain III and Jordan canonical form.

lecture 7: Structure of rings I. (Simple and primitive, Schur's Lemma).

lecture 8: Structure of rings II. (Density theorem, Wedderburn-Artin theorem).

lecture 9: Structure of rings III (Jacobson radical, semisimplicity).

lecture 10: Tensor product.

lecture 11: Chain conditions on modules.

lecture 12: Noetherian rings and primary decomposition

lecture 13: Noether Normalization Lemma and Hilbert's Nullstellensatz

lecture 14: Localization

lecture 15: Integral extensions, going up and going down theorem

lecture 16: Dimension theory

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Homeworks:

hw1    hw2    hw3    hw4    hw5    hw6    hw7    hw8    hw9    hw10    hw11    hw12    hw13    hw14