Details of MA4103 (Autumn 2017)

Level: 4 Type: Theory Credits: 4.0

Course CodeCourse NameInstructor(s)
MA4103 Algebra III Utsav Choudhury

Syllabus
1. Rings, ideals, quotient rings, homomorphisms and isomorphisms, prime ideals, maximal ideals, integral domains, field of fractions.

2. Modules, submodules, quotient modules, morphisms, tensor product, flat modules.

3. Chain condition.

4. Completion, localization, valuation.

5. Regularity, introduction to dimension theory.

References
1. Artin, M., Algebra, Prentice Hall, 1996.

2. Matsumura, H., Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, 1989.

3. Luthar, I. S. and Passi, I. B. S., Algebra: Volume 2: Rings, Narosa Publishing House, 2008 reprint.

4. Luthar, I. S. and Passi, I. B. S., Algebra: Volume 3: Modules, Narosa Publishing House, 2010 reprint.

5. Eisenbud, D., Commutative Algebra with a view towards Algebraic Geometry, GTM 151, Springer-Verlag, 1995.

Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Core
3 IP 5 Not Allowed
4 MR 1 Not Allowed
5 MR 3 Not Allowed
6 MS 7 Core
7 RS 1 Elective
8 RS 2 Elective