This is an undergraduate course on commutative algebra. Please read the course template for text-books and other important information about the course.
Grading :
Please note that there will not be any repeat class tests.
Recommended Reading:
Prerequisites: Vector Spaces, Rings and Modules (MTH 320)
Class timing:
Monday-5.30-6.30pm
Wednesday-9. 40-10.40am
Friday-2-3pm
Class room
LHC 304
Week 1
02/01/2019: Introduction to the course
04/01/2019:Ring homomorphism, ideals, quotients, zero divisors, nilpotents and units.
Week 2
07/01/2019: Prime ideals, maximal ideals ,existence of maximal ideals (Spectrum of a ring).
09/01/2019:Nilradical and Jacobson radical.
11/01/2019:Tutorial
Week 3
14/01/2019:Some properties of Ideals like Prime avoidance lemma, Chinese Remainder theorem and
colon of an ideal.
16/01/2019: Basic constructions for modules, like direct sums, direct products,
18/01/2019: Short test 1.
Week 4
21/01/2019:Short exact sequences,
23/01/2019:Hom functor
25/01/2019: Tutorial
Week 5
28/01/2019:Cayley-Hamilton theorem for endomorphisms of a finitely generated R- module , Nakayama's Lemma.
30/01/2019: Projective modules
01/02/2019: Class test 1.
Week 6
04/02/2019:Tensor products
06/02/2019: Flat modules.
08/02/2019: Short test II
Week 7
11/02/2019: Some more properties of projective modules.
13/02/2019: Tutorial.
15/02/2019: No class, please prepare for mid-sem exam.
Weak M
Mid-Semester examination, no class
Mid-sem on 25/02/2019
Week 8
25/02/2019: Mid-Sem exam
27/02/2019: Discussion on mid-sem exam; revision.
01/03/2019: Localization, important properties of localization like localization is an exact functor
Week 9
04/03/2019: Holiday
06/03/2019: Other important properties of localization like it commutes with tensor products, correspondence of prime ideals under localization.
08/03/2019: Tutorial.
Week 10
11/03/2019: No class; instructor will be at the International conference on number theory at the IISER, Tiruvananthapuram.
13/03/2019: Noetherian rings
15/03/2019: Short test 3.
Week 11
18/03/2019:Hilbert basis theorem and it's applications.
20/03/2019: Noetherian ring (properties)
22/03/2019: Tutorial.
Week 12
25/03/2019: Integral extensions
27/03/2019: Going up theorem.
29/03/2019:Class test II
Week 13
01/04/2019: Going down theorem.
03/04/2019: Applications of Integral extensions including Noether Normalization Lemma.
05/04/2019:Tutorial.
Week 14
08/04/2019: Primary decomposition.
10/04/2019: First uniqueness theorem of primary decomposition, Revision.
12/04/2019: Short test 4.
End of the course. The material taught in week 15 is for your intellectual satisfaction.
Week 15
These topics are not part of end- semester examination syllabus.
15/04/2019: Artin rings, revision.
17/04/2019: Holiday (Mahavir Jayanti)
19/04/2019: Holiday (Good Friday).
Week 16
End sem exam on 22/04/2019.
KINDLY MEET ME BEFORE 26TH APRIL, 2019 TO SEE END-SEM EXAM PAPER.