MSc pre-thesis talk
Time: 9.10 am, Friday Oct 14
Venue: Lecture Hall 5
Completion of Rings and Hensel's Lemma
Pratik Roy
Chennai Mathematical Institute.
14-10-22

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Abstract

I will define Completion of Topological Rings and give some examples. The talk will concentrate on the development of the theory of completion of rings along with some of its properties like exactness. The Noetherian property of a ring is a very important and desirable property, I will discuss briefly the fact that Completion of a Noetherian ring is Noetherian. As one of the most interesting properties of a complete ring, the Hensel's Lemma will be presented with proof. Due to time constraint all the proofs to the various lemmas and theorems required along the way are not included in the talk but some rough sketches are provided to some of them. As applications of the Hensel's Lemma I will be discussing about Lifting of idempotents for algebras over Noetherian complete rings and a version of the implicit function theorem in k[x,y].