Completion and Artin–Rees Lemma

Ghosh, Ahana (2025) Completion and Artin–Rees Lemma. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (Ahana Ghosh (23MP036)) 23MP036_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (8MB)

Abstract

The main purpose of this thesis is to discuss completion of polynomial, and to state and proof Artin Rees Lemma. We first discuss about some chapters named as Rings, Modules , Localization , Noetherian and Aritinan rings and modules. Then , we give some definition of graded rings , modules , filtered rings , modules. Then we proved Artin Rees Lemma , which depicts ,for an ideal I of a ring R, the I stable filtration of a R-module M, gives rise to I-stable filtration to its any submodule. Then we discussed about topological group and completion of topological groups . Finally , We showed that I adic filtration of polynomial ring R[X] is R[[X]], which is the ring of formal power series. Here I denotes (X).

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