NDSU

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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