1800 102 5661 [email protected]

Title Groups and Rings (Code 09010502)

S.N Unit Content Domain Hours as per UGC
1 one 1.    Definition of a group with example and simple properties of groups

2.    Subgroups and subgroup criteria

3.    Generation of groups, cyclic groups

4.    Cosets, Left and right cosets

5.    Index of a sub-group, Coset decomposition

6.    Lagrange’s theorem and its consequences

7.    Normal subgroups, Quotient groups

Must Know 15
2 Two 1.    Homoomorphisms

2.    Automorphisms of cyclic groups Groups

3.    Homoomorphisms

Must know 15
3 Three 1.    Introduction to rings, subrings, integral domains and fields,

2.    Characteristics of a ring. Ring homomorphisms, ideals (principle, prime and Maximal) and Quotient rings, Field of quotients of an integral domain.

3.    Euclidean rings, Polynomial rings, Polynomials over the rational field, , Polynomial rings over Unique factorisation domain

4.    R unique factorization domain implies so is R[X1,X2,…Xn] commutative rings,

Must know


Nice to know


Books Recommended;

  1. N. Herstein : Topics in Algebra, Wiley Eastern Ltd., New Delhi, 1975,
  2. B. Bhattacharya, S.K. Jain and S.R. Nagpal : Basic Abstract Algebra (2nd edition).
  3. Vivek Sahai and Vikas Bist : Algebra, NKarosa Publishing House.