Details of MA3102 (Autumn 2012)

Level: 3 Type: Theory Credits: 3.0

Course CodeCourse NameInstructor(s)
MA3102 Algebra I Himadri Mukherjee

Syllabus
MA3102 : Algebra I

Groups: Binary operations, groups and subgroups, examples, permutation groups and matrix groups; product of groups; group homomorphisms and isomorphisms : definitions and examples; equivalence relations and partitions, cosets, normal subgroups and quotient groups; Lagrange's theorem; cyclic groups; isomorphism theorems; finite direct product, direct sum of Abelian groups; group actions on sets with examples, conjugate classes, orbits and stabilizers, class equation; Cayley's theorem, Cauchy's theorem.

Rings: Definitions and examples of rings, zero divisors and units, integral domains and fields, polynomial rings and matrix rings; homomorphisms, ideals and quotient rings; integers modulo n and modular arithmetic; isomorphism theorems; prime ideals, maximal ideals; product of rings, ideals in a finite product; Chinese remainder theorem with applications; field of fractions of an integral domain; irreducible and prime elements; Euclidean domain, PID and UFD; factorization in Z[i]; properties of polynomial ring in one variable over a field.



References
Suggested Text/Reference Books:

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

2. Dummit, D. S. and Foote, R. M., Abstract Algebra (2nd Edition), Wiley (Student Edition), 2005.

3. Fraleigh, J. B., A First Course in Abstract Algebra (3rd Edition), Narosa Publishers, 1999.

4. Gopalakrishnan, N. S., University Algebra, New Age International, 1998.

5. Herstein, I. N., Topics in Algebra (3rd Edition), Wiley (Student Edition), 2006.

6. Hungerford, T. W., Algebra (2nd Edition), Graduate Texts in Mathematics, Volume 73, Springer-Verlag, 2003.

7. Musili, C., Introduction to Rings and Modules, Narosa Publishers, 1999.

8. Sen, M. K., et al., Topics in Abstract Algebra (2nd Edition), Universities Press, 2006.



Course Credit Options

Sl. No.ProgrammeSemester NoCourse Choice
1 IP 1 Not Allowed
2 IP 3 Not Allowed
3 MS 5 Not Allowed
4 RS 1 Not Allowed