Syllabus
|
Course Code: B-MAT 401 Course Name: Abstract Algebra |
||
| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
|---|---|---|
| 1 | Definition and examples of a group including Permutation group, quaternion group, Abelian and Nonabelian groups. The Group Zn of integers under addition modulo n and under multiplication modulo n . Elementary properties of groups. Order of a group. Order of an element of a group . Subgroup and Subgroup tests. Centralizer, Normalizer, Center of a group. Cyclic group and properties of cyclic groups. Cycle notation for permutations. Properties of permutations. Even and odd permutations. Alternating groups. | |
| 2 | Cosets. Index of a subgroup , Lagrange’s theorem , Normal subgroup , Quotient groups . Group homomorphism, Group isomorphisms. Cayley’s theorem. Properties of isomorphisms. First, Second and Third isomorphism theorems for groups. | |
| 3 | Definition and examples of rings. Commutative and non-commutative rings. Rings from number system ,Zn ring of integers modulo n , Ring of matrices. Properties of rings. Subrings. Characteristic of a ring. Integral Domain and Field. Examples of fields: Zn, Q, R and C. Ideals. Ideal generated by a subset of a ring. Prime and maximal ideals. | |
| 4 | Quotient ring. Ring homomorphisms. Properties of ring homomorphisms. First, Second and Third Isomorphism theorems for rings. Euclidean ring. | |
