Integrated MSc-PhD Program

SYLLABUS

KSM2C01: Algebra II
 

More Group Theory: The Classical Groups, Spheres, The Groups SU_2 SO_3, One-Parameter Groups, The Lie Algebra, Translation in a Group, Normal Subgroups of SL_2, Definition of a Ring, Polynomial Rings, Homomorphisms and Ideals, Quotient Rings, Adjoining Elements, Product Rings, Fractions, Maximal Ideals, Factoring Integers, Unique Factorization Domains, Gauss’s Lemma, Factoring Integer Polynomials, Gauss Primes, Modules, Free Modules, Identities, Diagonalizing Integer Matrices, Generators and Relations, Noetherian Rings, Structure of Abelian Group, Application to Linear Operators, Polynomial Rings in Several Variables.

Suggested texts:

            1. Michael Artin, Algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991. (Chapters 9,11,12,14)
            2. Serge Lang, Algebra, third ed., Graduate Texts in Mathematics, vol. 211, Springer-Verlag, New York, 2002.
            3. David S. Dummit and Richard M. Foote, Abstract algebra, Prentice Hall, Inc., Englewood Cliffs, NJ, 1991.
            4. Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, New York-Berlin, 1980, Reprint of the 1974 original.