ALGEBRA
Groups: Review of Groups, Subgroups, Homomorphisms, Normal subgroups, Quotient groups, Isomorphism theorems. Group actions and its applications, Sylow theorems. Structure of finitely generated abelian groups, Free groups. Rings: Review of rings, Homomorphisms, Ideals and isomorphism theorems. Prime ideals and maximal ideals. Chinese remainder theorem. Euclidean domains, Principal ideal domains, Unique factorization domains. Factorization in polynomial rings. Modules: Modules, Homomorphisms and exact sequences. Free modules. Hom and tensor products. Structure theorem for modules over PIDs.
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