Duke University

Paul Aspinwall
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Mathematics
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C.G.T.P.
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Duke University

Commutative Algebra
(Math 252)

Spring 2009

Instructor: Paul Aspinwall

Credits: 1.00, Hours: 03.0

Time: MWF, 1:30-2:20pm (occasionally 1:15-2:30pm).

Location: Physics 205

Math 251, or consent from me.

A rough outline is as follows

Ideals
- Localization
- Gröbner and standard bases
Modules
- Standard Bases
- Free Resolutions
- Tensor Product
- Intersections, quotients, etc.
Noether Normalization
Primary Decomposition
The Hilbert Polynomial

In all of the above connections with algebraic geometry will be discussed. Singular will be used extensively.

The course will be based on:

G.-M. Greuel and G. Pfister, A Singular Introduction to Commutative Algebra, Springer 2002.

It may also be useful to refer to

D. Cox, J. Little, D. O'Shea, Ideals, Varieties, and Algorithms, Springer 1992.
David Eisenbud, Commutative Algebra with a View Toward Algebraic Geometry, Springer 1999.
M. Atiyah, MacDonald, Introduction to Commutative Algebra, Addison-Wesley 1969.
R. Hartshorne, Algebraic Geometry, Springer 1977.

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C.G.T.P.
Duke University, Box 90318
Durham, NC 27708-0318