Speakers :
Sr. | Name | Affiliation |
1 | Amartya Kumar Dutta | ISI Kolkata |
2 | Dilip Patil | IISc Bangalore |
3 | Ananthnarayan Hariharan | IIT Bombay |
4 | S. M. Bhatwadekar | Bhaskaracharya Pratishthan, Pune |
5 | Ganesh Kadu | Savitribai Phule Pune University |
Course associates :
Sr. | Name | Affiliation |
1 | Asawari Abhyankar | IIT Bombay |
2 | Dilpreet Kaur | |
3 | Deepa Krishnamurthi | MIT College, Pune |
4 | Jatin Majithia | College of Engineering Pune |
Syllabus :
Module-1 : Affine Space and Algebraic Sets, The Ideal of a Set of Points, Hilbert Basis Theorem, Irreducible Components of an Algebraic Set, Varieties, Radical Ideals, Hilbert’s Nullstellensatz, Coordinate Rings, Krull dimension of ring.
Module-2 : Extension and Contraction of ideals, Nilradical, Jocobson radical, Noetherian rings, Artinian rings, primary decomposition of ideals.
Module-3 : Localization, Integral extensions, going up theorem, Noether’s Normalization lemma, rings of algebraic integers, Dedekind domains.
Module-4: Modules, definition and examples, operations on modules, direct sum and products, finitely generated modules, free modules, Nakayama’s lemma.
Abstract of the Lectures :
(i) Amartya Kumar Dutta : Affine Space and Algebraic Sets, The Ideal of a Set of Points, Hilbert Basis Theorem, Irreducible Components of an Algebraic Set, Varieties, Radical Ideals.
(ii) S. M. Bhatwadekar: Hilbert’s Nullstellensatz, Coordinate Rings, Krull dimension of ring, localization.
(iii) Dilip Patil : Extension and Contraction of ideals, Nilradical, Jacobson radical, Noetherian rings, Artinian rings, primary decomposition of ideals.
(iv) Ananthnarayan Hariharan : Integral extensions, going up theorem, Noether’s Normalization lemma, rings of algebraic integers, Dedekind domains.
(v) Ganesh Kadu : Modules, definition and examples, operations on modules, direct sum and products, finitely generated modules, free modules, Nakayama’s lemma.
References :
i) Commutative Algebra, N.S. Gopalkrishnan.
ii) Introduction to Commutative Algebra, M.F. Atiyah and I G Mcdonald.
First Week : 28th Novt o 3rd December 2016
Day | 9:30- 11:00 | 11:00- 11:30 | 11:30- 1:00 | 1:00- 2:30 | 2:30-3:30 | 3:30- 4:00 | 4:00-5:00 | 5:00- 5:30 |
Mon | AD | Tea | DP | Lunch | AD/JM/DKM | Tea | AD/JM/DKM | Snacks |
Tue | AD | Tea | DP | Lunch | DP/JM/DKM | Tea | DP/JM/DKM | Snacks |
Wed | AD | Tea | DP | Lunch | AD/JM/DKM | Tea | AD/JM/DKM | Snacks |
Thu | AD | Tea | DP | Lunch | DP/JM/DKM | Tea | DP/JM/DKM | Snacks |
Fri | AD | Tea | DP | Lunch | AD/DK/AA | Tea | AD/DK/AA | Snacks |
Sat | GK | Tea | SMB | Lunch | DP/DK/AA | Tea | DP/DK/AA | Snacks |
Second Week : 5th Dec to 10th Dec 2016
Day | 9:30- 11:00 | 11:00- 11:30 | 11:30- 1:00 | 1:00- 2:30 | 2:30-3:30 | 3:30- 4:00 | 4:00-5:00 | 5:00- 5:30 |
Mon | AH | Tea | GK | Lunch | GK/JM/DKM | Tea | GK/JM/DKM | Snacks |
Tue | AH | Tea | SMB | Lunch | AH/DK/AA | Tea | AH/DK/AA | Snacks |
Wed | AH | Tea | GK | Lunch | AH/DK/AA | Tea | AH/DK/AA | Snacks |
Thu | AH | Tea | SMB | Lunch | GK/DK/AA | Tea | GKDK/AA | Snacks |
Fri | AH | Tea | GK | Lunch | AH/AA/GK | Tea | AH/AA/GK | Snacks |
Sat | GK | Tea | SMB | Lunch | GK/AA/JM | Tea | GK/AA/JM | Snacks |
- AD: Amartya Kumar Dutta
- SMB: S. M. Bhatwadekar
- JM: Jatin Majithia
- AA: Asawari Abhyankar
- DP: Dilip Patil
- AH: Anathnarayan Hariharan
- GK : Ganesh Kadu
- DK: Dilpreet Kaur
- DKM: Deepa Krishnamurthi