Subject Code: MA5L006 Subject Name: Algebra L-T-P: 3-1-0 Credit:4
Pre-requisite(s): Linear Algebra  (MA5L001)
Groups: Binary operation and its properties, Definition of a group, Examples and basic properties, Subgroups, Cyclic groups, Dihedral Groups, Permutation groups, Cayley’s theorems. Coset of a subgroup, Lagrange’s theorem, Order of a group, Normal subgroups, Quotient group, Homomorphisms, Kernel Image of a homomorphism, Isomorphism theorems, Direct product of groups, Group action on a set, Semi-direct product, Sylow’ theorems, Structure of finite abelian groups.
Rings: Definition, Examples and basic properties. Zero divisors, Integral domains, Fields. Characteristic of a ring, Quotient field of an integral domain. Subrings, Ideals, Quotient rings, Isomorphism theorems, Ring of polynomials. Prime, Irreducible elements and their properties, UFD, PID and Euclidean domains. Prime ideal, Maximal ideals, Prime avoidance theorem, Chinese remainder theorem.
Fields: Field of fractions, Gauss lemma, Fields, field extension, Galois theory.
Text Books:
  1. Gilbert W. J.  and Nicholson W. K.  Modern Algebra with Applications, Wiley
  2. Dummit D.  and Foote R.  Abstract Algebra, Wiley
Reference Books:
  1. Artin. Algebra, Prentice-Hall of India
  2. Herstein, Topics in Algebra, Wiley
  3. Herstein, Abstract Algebra, Wiley
  4. Gallian, Contemporary Abstract Algebra, Narosa
  5. Fraleigh J. B. A First Course in Abstract Algebra, Pearson