Algebra -I

Unit 1- A brief review of groups, their properties and examples, subgroups, cyclic groups, normal
subgroups, quotient groups, symmetric, alternating, and dihedral groups, homomorphism and
isomorphism theorems.
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Unit 2- Group action, orbits and stabilizers, class equations and its applications, direct products,
semi-direct products, permutation groups, Lagrange‟s theorem, Cayley‟s theorem, and
Sylow‟s theorem
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Unit 3- Introduction to rings, homomorphisms, ideals and quotients, prime and maximal ideals,
principal ideal domain, unique factorization domain, polynomial rings and irreducible
criteria, Euclidian domain.
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Unit 4- Fields, field extensions, algebraic extensions, roots of a polynomial, simple, separable,
inseparable, and purely separable extensions, finite fields, perfect and imperfect fields.
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Unit 5- chapter 5View Link

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