This course is to provide  the background for students who are willing to learn more about rings and modules which are  the fundamental mathematical structures occuring everywhere !  It is useful for everyone but especially for students who are planning to study  any  algebra related topics such as algebraic topology, algebraic geometry, analysis.

Approximately half of the semester will be on rings, the second half will be on modules.  Rings will be  a more detailed but much faster version of some of the topics  you have seen in Math 367, and  Math 116.   Modules will be new to you. They are generalizations of  vector spaces also generalization of abelian groups.  (Modules over group algebras|rings are examples of groups acting on vector spaces.)

Thus in  module theory  linear algebra comes up  quite often.  You should be comfortable using linear algebra to get more out of this course. We will see the primary decomposition theorem for  finitely generated modules over a Euclidean domain. Usually there is not enough time to cover tensor products.