Math 793 Summer 2003
Below I have included a copy of the course syllabus and links to
the homework assignments.
Here is a tentative outline.
Week 1 Review of basic notions of ring theory. Ideals, prime,
radical, maximal ideals. Multiplicative sets. Noetherian rings.
Week 2 Localizations and correspondence theorems. Valuations
and valuation domains.
Week 3-4 Integral and almost integral extensions. Integral
closure and connections with valuations. Ideal correspondence in
integral extensions.
Week 5-6 Polynomial and A+xB[x] extensions. General D+M
constructions. Hilbert basis theorem and some consequences. Dimension
of polynomial extensions.
Week 6-7 Power series extensions. Dimension theory. Basis
theorem for power series.
Week 8 Generalized completions. I-adic completions.
Here is the syllabus.
Here are the homeworks.
Homework 1
Homework 2
Homework 3
Homework 4
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