Algebra (Abstract)

Good Books for reference:

  1. Contemporary abstract algebra (Joseph A. Gallian)

  2. Topics in Algebra (I. N. Herstein)


Syllabus for Algebra

Groups

Subgroups

Normal subgroups

Quotient groups

Homomorphisms

Automorphisms

Cyclic groups

Permutation groups

Sylow’s theorems and their applications

Rings

Ideals

Prime and maximal ideals

Quotient rings

Unique factorization domains

Principle ideal domains

Euclidean domains

Polynomial rings and irreducibility criteria

Fields

Finite fields

Field extension



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