**Date & Time:** Monday, August 24, 2009, 15:30-17:00.

**Venue:** Room 215

**Title:** Injective Hulls Matlis Duality - I

**Speaker:** Shreedevi Masuti, IIT Bombay

**Abstract:** Any module *M* can be embedded into an injective module *E*. Such an embedding can be chosen to be minimal. In this case, *E* is uniquely determined and it is called the injective hull of *M*. Over a Noetherian ring *R*, any module can be decomposed uniquely as a direct sum of indecomposable injective modules. Indecomposable injective modules turn out to be injective hulls of *R/P* where *P* is some prime ideal of *R*. If *R* is local with maximal ideal and *E* is the injective hull of *R*/, then the functor Hom(-, *E*) establishes an anti-equivalence between the category of Artininan *R*-modules and the category of finite *R*-modules. This is known as Matlis duality which plays a fundamental role in the study of Gorenstein rings.