### Mathematics 551 Abstract Algebra Fall 2006

This will be a basic graduate algebra course discussing such algebraic
structures as categories, monoids and groupoids, groups, rings, and
modules. Since categories form a basic structure having many
applications as diverse as physics or computer science, we will begin
there. Examples of algebraic objects will be emphasized throughout,
as well as connections with other areas of mathematics.
This is an introduction to the mathematics of groups, rings and
modules. The concept of groups acting on vector spaces will be used
as a unifying idea which illustrates the interplay of these topics
Examples that provide concrete interpretation of the theory will be
discussed.
Topics will include the following :
basic properties of groups, rings and modules

rings, ideals, chain conditions

modules over principal ideal domains, including abelian groups

Categories and functors
Groups and homomorphisms
Groups acting on sets and vector spaces
Rings, ideals and principal ideal domains and chain conditions
Modules, homomorphisms and structure theorems for modules over
principal ideal domains

This is an introduction to the mathematics of groups, rings and
modules. The concept of groups acting on vector spaces will be used
as a unifying idea which illustrates the interplay of these topics
Examples that provide concrete interpretation of the theory will be
discussed.

Prerequisites: A standard undergraduate knowledge of algebra
is required. It will be assumed that students understand the concepts
of group, ring, vector space and linear algebra,
and simple notions of groups and rings

Text: The text for this course will be Algebra by
T Hungerford (GTM 73)

Course Format: There will be weekly homework assignments, and
midterm and final exams.

More Information: Contact J. Tunnell in Hill 546, or email to
tunnell@math