Title: Modules vs Vector Spaces
Speaker: Kumari Saloni
Date: September 09, 2015; September 11, 2015 and September 14, 2015
Time: 11:00 AM
Venue: Discussion Room
ABSTRACT: In linear Algebra, the most important structure is that of a vector space over a field. It is interesting to consider the generalization of this concept to the case where field is replaced by a commutative ring. The resulting structure is called module. In principle, we expect an anlogous theory for modules, but we will see that many basic concepts in case of vector spaces, for example dimension, cannot be generalized as it is for modules. We will introduce and discuss basic theory of modules in these series of talks. We will discuss a generalization of Cayley-Hamiltom theorem for modules. As a consequence, we will prove Nakayama Lemma which is a most frequently used tool in Commutative Algebra.