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Advanced Abstract Algebra [1]

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: 
  1. Chauhan & Singh, Advanced Abstract Algebra, JPH, Jaipur.
  2. P.B.Bhattacharya, S.K.Jain and S.R.Nagpaul,Basic Abstract Algebra , Cambridge     University Press.
  3. I.N.Herstein , Topics in Algebra , Wiley Eastern Ltd., New Delhi
  4. J.B.Fraleigh: Abstract Algebra, Narosa Pvt. Ltd.
 
References: 
  1. Deepak Chatterjee,Abstract Algebra.PHI. Ltd.New Delhi.
  2. Malcolm Birkoff ,Abstract Algebra , Cambridge University Press
 
Academic Year: 
2014-2015 [2]

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[1] https://maths.iisuniv.ac.in/courses/subjects/advanced-abstract-algebra-2
[2] https://maths.iisuniv.ac.in/academic-year/2014-2015