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Full Description
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.
Contents
Course I: Classical formulas
Classical number theory
Commutative rings
Groups
Galois theory
Appendix: Set theory
Appendix: Linear Algebra
Course II: Modules
Zorn's lemma
Advanced linear algebra
Categories of modules
Multilinear algebra
Commutative algebra II
Appendix: Categorical limits
Appendix: Topological spaces
Bibliography
Special notation
Index
