ABSTRACT ALGEBRA HAND WRITTEN NOTES IN PDF FOR CSIR NET /GATE/IIT JAM , Lecture notes for abstract algebra

            ABSTRACT ALGEBRA

ABSTRACT ALGEBRA HAND WRITTEN NOTES IN PDF 
FOR CSIR NET /GATE/IIT JAM 

SYLLABUS:

 *Permutations & Combinations,

 *pigeon-hole principle, inclusion-exclusion principle, derangements. 

*Fundamental theorem of arithmetic, divisibility in Z, congruences,

 *Chinese Remainder Theorem,

*Euler’s Ø- function,

* primitive roots.

*Groups, subgroups, normal subgroups, quotient groups,

* homomorphisms, cyclic groups, permutation groups,

*Cayley’s theorem,

*Class equations and Sylow theorem.

*Rings, ideals, prime and maximal ideals, quotient rings,

* Unique factorization domain, Principal ideal Domain ,

*Euclidean domain.

*Polynomial rings and irreducibility criteria.

*Fields, finite fields, field extensions, Galois Theory.

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