Advanced Abstract Algebra
Paper Code:
MAT121
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
Unit I:
1
15.00
Direct product of groups (External and Internal). Isomorphism theorems - Diamond isomorphism theorem, Butterfly Lemma, Conjugate classes, Sylows theorm, p- sylow theorem .
Unit II:
II
15.00
Commutators, Derived subgroups, Normal series and Solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite groups.
Unit III:
III
15.00
Polynomial rings, Euclidean rings. Modules, Submodules, Quotient modules Direct sums and Module Homomorphisms. Generation of modules, Cyclic modules.
Unit IV:
IV
15.00
Field theory - Extension fields, Algebraic and Transcendental extensions, Separable and inseparable extensions, Normal extensions. Splitting fields. Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory,
Unit V:
V
15.00
Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory , Solvalibility by radicals.
Essential Readings:
- Chauhan & Singh, Advanced Abstract Algebra, JPH, Jaipur.
- P.B.Bhattacharya, S.K.Jain and S.R.Nagpaul,Basic Abstract Algebra , Cambridge University Press.
- I.N.Herstein , Topics in Algebra , Wiley Eastern Ltd., New Delhi
- J.B.Fraleigh: Abstract Algebra, Narosa Pvt. Ltd.
References:
- Deepak Chatterjee,Abstract Algebra.PHI. Ltd.New Delhi.
- Malcolm Birkoff ,Abstract Algebra , Cambridge University Press
Academic Year:
