Abstract
In this series of lectures I will give an introduction to
semidualizing modules over commutative noetherian rings. I will
present aspects of the theory behind these objects and some of their
applications within the study of rings and ring homomorphisms.
I will begin by motivating the definition of the semidualizing
property with a survey of some aspects of homological commutative
algebra. I will then discuss methods for constructing examples of
semidualizing modules and prove some of their basic properties. I will
continue by introducing the Auslander and Bass classes associated to a
semidualizing module and discussing the properties of these classes.
It is these classes which give the semidualizing modules much of their
power. The Bass classes give a way to endow the set of semidualizing
modules over a fixed ring with the structure of an ordered set. An
analysis of the ordering yields the first application which gives a
lower bound for the growth of the Bass numbers of a local
CohenMacaulay ring.
Next I will discuss the Gorenstein dimension associated to a
semidualizing module and, specifically, the Gdimension of a local
ring homomorphism. This will allow me to give three more applications:
(1) existence of the Bass series for a local homomorphism of finite
Gdimension; (2) additional structure for quasideformations
associated to modules of finite CIdimension; and (3) a special case
of the composition question for local ring homomorphisms of finite
Gdimension.
Information:
Date:  Wednesday, July 9 to Monday, July 14, 2008, Morning sessions: 10:0011:00, Afternoon sessions: 14:0015:00  Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
