Commutative Algebra I

Catalog description

This course deals with fundamentals and basic techniques of Commutative Algebra. This can be a good introduction to Algebraic Geometry and Algebraic Number theory. The course begins with Rings, Ideals, Modules, Localization. Homological Algebra with concepts leading to Flatness, Dimension, Depth, Ascending and Descending Chain Conditions and Completion would be some of the typical material covered in this course, although other topics may be introduced as well. Topics such as Cohen-Macaulay Rings, Normal Rings, Regular Rings, Gorenstein Rings, Noether Normalization, Primary Decomposition, etc. may be covered if time permits or will be continued in the second part of the course. Credit Hour s : 3 Prerequisites: MATH 8410 and MATH 8411 or equivalent