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ABSTRACT ALGEBRA [1]

Paper Code: 
MAT501
Credits: 
3
Contact Hours: 
45.00
Max. Marks: 
100.00
Unit I: 
I
9.00
Definition of a group with examples and simple properties. Order of elements in a Group and related theorem.
 
Unit II: 
II
9.00

Subgroups ,Cyclic groups, Permutation groups  , Alternating group

Unit III: 
III
9.00
Cosets, Lagrange’s theorem Normal subgroups , Quotient group.
 
Unit IV: 
IV
Homomorphism and Isomorphism, the Fundamental theorem of  homomorphism. Rings:-Definition, Examples and Elementary properties.   
 
 
Unit V: 
V
9.00
Integral domain, Fields, Subfields and their simple properties, Subrings. Ideal of a ring, Characteristic of a ring.
Essential Readings: 
  1. K. C. Sarangi , Elements of Abstract Algebra, RBD, Jaipur, 2009.
  2. P.B.Bhattacharya , S.K.Jain and S.R.Nagpaul,Basic Abstract Algebra , Cambridge     University Press, 2001.
  3. G. C. Sharma , Modern Algebra, Shivlal Agarwal & Co. Agra, 1998.
References: 
  1. Deepak Chatterjee,Abstract Algebra.PHI. Ltd.New Delhi.
  2. I.N.Herstein , Topics in Algebra , Wiley Eastern Ltd., New Delhi
  3. Malcolm Birkoff ,Abstract Algebra , Cambridge University Press
 
Academic Year: 
2015-2016 [2]

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[1] https://maths.iisuniv.ac.in/courses/subjects/abstract-algebra-3
[2] https://maths.iisuniv.ac.in/academic-year/2015-2016