Course Information

We will study Groups, Rings, and Modules, assuming some knowledge of undergraduate level algebra. So the students are assumed to have seen the basics of these objects before. A list of topics to be covered is as follows:

* Review of basics of group theory: definition, examples, homomorphisms, subgroups, quotient groups, etc.

* Group actions.

* Sylow Theorems.

* Solvable groups.

* Nilpotent groups.

*Review of basics of rings\dots

* Chinese Remainder Theorem.

*uclidean domains, PIDs, UFDs.

* Polynomial rings.

* Basics of modules\dots

* Tensor product of modules.

*Exact sequences of modules.

* Modules over PIDs.