Programmes → I.M.Sc. in Mathematical Sciences; M.Sc. Mathematics/Applied Mathematics

Algebra-II

Course Code: MA 360; MM 454 | Credits: 4 | Prerequisite: Linear Algebra, Algebra-I

Unit I: Basic concepts in rings, ideals, homomorphism of rings, quotients with several examples.
Unit II: Euclidean domains, principal ideal rings/domains, factorization domains and unique factorization domains.
Unit III: Eisenstein’s irreducibility criterion and Gauss’s lemma.
Unit IV: Modules, Modules over PIDs, Modules with chain conditions, Hilbert Basis Theorem.
Unit V: Field extensions, algebraically closed fields, finite fields, Ruler and compass techniques etc.

Learn definition and basics of rings, ideals, homomorphisms between rings (Apply).
Learn important classes of rings like Euclidean Domains, Principal Ideal Domains, Unique Factorization Domains (Apply).
Learn all about polynomial rings over rings, fields, irreducible polynomials over fields and rings (Apply).
Learn definition and basics of modules, move on to study modules over special rings (Apply).
Learn elementary properties of field extensions, algebraic closure, existence of algebraic closure of any field, applications to geometry (Apply).

Artin, Michael, Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991.
Herstein, I.N. Topics in Algebra, 3rd ed. Wiley, New York, 1996.
Dummit, David S. and Foote Richard M., Abstract Algebra, third edition, John Wiley & Sons, Inc., Hoboken, NJ, 2004.
Jacobson, Nathan, Basic Algebra, Volume 1, second edition, W. H. Freeman and Company, New York, 1985.
Musili, C., Introduction to Rings and Modules, Narosa, 1992.