Course:MATH600D 17/18II
Faculty of Science Department of Mathematics 


MATH 600 / D Topics in Algebra 

Instructor:  Sujatha Ramdorai 
Office:  MATH Annex 1201 
Class schedule:  Tue Thu 11:00 am  12:30 pm 
Classroom:  MATH Annex 1102 
Office hours:  
Course pages  
No pages found. 
In this course, we plan to cover some parts of Commutative Algebra that are used in Algebraic Number Theory and Algebraic Geometry. Some of these topics will include Integral closure, Dedekind domains and Discrete valuation rings. We will then cover some ground from Homological Algebra, primarily leading to the concept of homological dimension of Noetherian rings. This will be used to state the AuslanderBuchsbaum Theorem on regular local rings and provide an overview of key steps in the proof. The aim is to make the course as selfcontained as possible. Students are definitely expected to be familiar with the material covered in Algebra I (Course no. 501). Some exposure to Homological Algebra will be helpful, though not strictly necessary. Grades will be based on class participation, engagement, exercises and lectures. The participants are expected to give one or two lectures along the course. There is no prescribed text book. The books listed in the References section will be helpful for the students
Homework
 Homework 1 Due Tuesday, Feb 6th
 Remarks Remarks on Homework 1 Problems
 Homework 2 Due Tuesday, Feb 27th
 Homework 3 Due Thursdaay, March 22nd
Student Lectures
 Projective and Flat Modules and Noetherian Rings First Topic for Presentation
 Second Topic for Presentation
 3rd and 4th Topics
Lecture Details
Lecture Date 
Topics Covered  Notes  

1 
4/1

Integral Extensions  Class 1 notes 
2 
9/1

Integral Extensions (contd.)  
3 
11/1

Norms and Traces, Spectrums of Int. Extns  
4 
16/1

Height, Dimension and Localization  
5 
18/1

Projective Dimension, Going Up and Down  
6 
23/1

Going Down (contd.), Flat Extensions  
7 
25/1


8 
30/1

UFDs  
9 
1/2

Discrete Valuation Rings; Noetherian Modules (Coco's talk)  Coco's talk 
10 
6/2

Normal and Dedekind domains  
11 
8/2

Projective and Flat Modules: Coco and Ashvni 
References
 M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra. AddisonWesley Publishing Company, Inc.
 H. Matsumara, Commutative Algebra. W.A. Benjamin.
 E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry. Springer.
 C. Weibel, An Introduction to Homological Algebra. Cambridge University Press.
 TIFR Pamphlet on Homological Algebra