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# algebrasyllabus - Modules isomorphism theorems finitely...

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Syllabus for Preliminary Exam for 631-632 Algebra I, II Linear algebra: vector spaces, linear transformations, eigenvectors and diagonalization, Jordan canonical form, bilinear forms and inner product spaces, normal operators. Groups: cosets, quotient groups, isomorphism theorems, group actions, Sylow theorems, finitely generated abelian groups. Rings: ideals, quotients, isomorphism theorems, principal ideal domains, unique factorization domains, Euclidean domains, integers and polynomials.
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Unformatted text preview: Modules: isomorphism theorems, finitely generated modules over principal ideal domains. Fields: field extensions, algebraic and transcendental elements and extensions, Galois theory. Suggested textbook: M. Artin, Algebra Chapter 2, 3, 4(sections 1-4, 6), 5(sections 5-7), 6(sections 1, 3-6), 7(sections 1-5), 10(sections 1-7), 11(sections 1-4), 12(sections 1-7), 13(sections 1-3,5,6), 14 (sections 1-5)....
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