Course No
MA601
Credit
8
Syllabus
Group Theory: Dihedral groups, Permutation groups, Group actions, Sylow’s theorems, Simplicity of the alternating groups, Direct and semidirect products, Solvable groups, Nilpotent groups, Jordan Holder Theorem, free groups.
Ring Theory: Properties of Ideals, Chinese remainder theorem, Field of fractions, Euclidean domains, Principal ideal domains, Unique factorization domains, Polynomial Rings, Irreducibility criteria, Matrix rings.
Module Theory: Examples, quotient modules, isomorphism theorems, Generation of modules, free modules, tensor products of modules, Exact sequences - Projective, Injective and Flat modules.
Reference Books
- D. S. Dummit and R. M. Foote, Abstract Algebra. John Wiley & Sons, 2004.
- T. W. Hungerford, Algebra, Graduate Texts in Mathematics, 73, Springer, 1980.
- M. Artin, Algebra, Prentice Hall, 1991.
- N. Bourbaki, Algebra, Springer, 1989.
- C Musili, Introduction to Rings and Modules, Narosa Publishing House.
- N. S. Gopalakrishnan, University Algebra, New Age International