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9781470480998 Academic Inspection Copy

Advanced Modern Algebra

Part 1
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This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Grobner bases.
Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.
Part A. Course I Chapter A-1. Classical formulas Chapter A-2. Classical number theory Chapter A-3. Commutative rings Chapter A-4. Groups Chapter A-5. Galois theory Chapter A-6. Appendix: Set theory Chapter A-7. Appendix: Linear Algebra Part B. Course II Chapter B-1. Modules Chapter B-2. Zorn's lemma Chapter B-3. Advanced linear algebra Chapter B-4. Categories of modules Chapter B-5. Multilinear algebra Chapter B-6. Commutative algebra II Chapter B-7. Appendix: Categorical limits Chapter B-8. Appendix: Topological spaces
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