**Date & Time:** Monday, August 19, 2013, 15:30-17:00.

**Venue:** Ramanujan Hall

**Title:** Injective Modules and Matlis Duality IV

**Speaker: ** Ananthnarayan Hariharan, IIT Bombay

**Abstract:**In the study of injective modules over Noetherian local rings, the
work of Matlis shows that it is enough to study injective hulls of the residue
fields. This study leads is to a duality between Artinian modules over a
Noetherian ring and Noetherian modules over its completion, called Matlis
duality. In this series of talks, we will begin with a quick review injective
modules and injective hulls over a commutative ring. We will then proceed to
the study of indecomposable injective modules over a Noetherian local ring,
finishing with Matlis duality.