MALAVIYA NATIONAL INSTITUTE OF TECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
SYLLABUS
MAT-611
Abstract Algebra
4 Credits( 3L+1T+0P)
Groups: Normal subgroups, quotient groups, homomorphism and isomorphism theorems of
groups. Maximal subgroups. Composition series of a group. Direct product. Cauchy’s and
Sylow’s theorems for finite groups.
Rings: Subrings and Ideals. Principal and Maximal Ideals. Quotient rings, isomorphism of
rings, characteristic of a ring. Imbedding of a ring into another ring. Polynomial rings.
Irreducible polynomials. Division algorithm for polynomials over a field. Euclidean
algorithm. Euclidean algorithm for polynomial over a field. Euclidean rings. Properties of
Euclidean rings. Unique factorization domains.
Fields: Simple and algebraic field extensions. Splitting fields and normal extensions. Finite
fields and applications.
Books Recommended:
1. Algebra I, II &III, R.K Sharma et al., Pearson.
2. Algebra, S. Lang, Springer.
3. Algebra, M. Artin, PHI Learning.
4. Topics in Algebra, I.N. Herstein, Wiley India Pvt. Ltd.