ADVANCED ABSTRACT ALGEBRA
Paper Code:
MAT121
Credits:
5
Contact Hours:
75.00
Max. Marks:
100.00
15.00
Direct product of groups (External and Internal). Isomorphism theorems - Diamond isomorphism theorem, Butterfly Lemma, Conjugate classes.
15.00
Commutators, Derived subgroups, Normal series and Solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite group
15.00
Modules, Submodules, Quotient modules Direct sums and Module Homomorphisms. Generation of modules, Cyclic modules.
15.00
Field theory - Extension fields, Algebraic and Transcendental extensions, Separable and inseparable extensions, Normal extensions. Splitting fields.
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.III Edition,2011
- P.B.Bhattacharya, S.K.Jain and S.R.Nagpaul,Basic Abstract Algebra , Cambridge University Press, II Edition,1995
- I.N.Herstein , Topics in Algebra , Wiley Eastern Ltd., New Delhi, II Edition,1975
- J.B.Fraleigh, Abstract Algebra, Narosa Pvt. Ltd.
References:
- Deepak Chatterjee,Abstract Algebra.PHI. Ltd.New Delhi. III Edition,2015.
- John B. Fraleigh, A First Course in Abstract Algebra, Pearson New International II Edition 2003.
Academic Year:
