Mathematics 6150

Commutative Algebra

Course Description
Introduces topics used in number theory and algebraic geometry, including radicals of ideals, exact sequences of modules, tensor products, Ext, Tor, localization, primary decomposition of ideals, and Noetherian rings. Prereq., MATH 6140. Undergraduates must have approval of the instructor.
Schedule MWF 9 - 10 AM,  ECCR 110
(University of Colorado Academic Calendar)
Sebastian Casalaina-Martin
Mathematics 221
Office Hours
T 9 AM - 12  PM or by appointment.
We will work primarily from:

1.  Atiyah, M. F. and MacDonald, I. G. Introduction to commutative algebra. Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont. 1969 ix+128 pp.

2.  Altman, A. and  Kleiman, S. Introduction to Grothendieck duality theory.  Lecture Notes in Mathematics, Vol. 146 Springer-Verlag, Berlin-New York 1970 ii+185 pp.

Some other introductory books on the subject:

3.  Matsumura, H. Commutative ring theory. Translated from the Japanese by M. Reid. Second edition. Cambridge Studies in Advanced Mathematics, 8. Cambridge University Press, Cambridge, 1989. xiv+320 pp

4.  Eisenbud, D. Commutative algebra. With a view toward algebraic geometry. Graduate Texts in Mathematics, 150. Springer-Verlag, New York, 1995. xvi+785 pp.

5. Bourbaki, N. Commutative algebra. Chapters 17. Translated from the French. Reprint of the 1989 English translation. Elements of Mathematics (Berlin). Springer-Verlag, Berlin, 1998. xxiv+625 pp.

There will be homework assignments posted online.
This syllabus is a rough guide to the topics we will cover.
Please read the following class policies.