Commutative Algebra (Math 252)
Spring 2009
Instructor:
Paul Aspinwall
Credits: 1.00, Hours: 03.0
Time: MWF, 1:302:20pm (occasionally 1:152:30pm).
Location: Physics 205
Requirements
Exams
Prerequisits
Math 251, or consent from me.
Synopsis
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.
Textbooks
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, AddisonWesley 1969.
 R. Hartshorne, Algebraic Geometry, Springer 1977.
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