(Graduate Studies in Mathematics 165) Joseph J. Rotman-Advanced Modern Algebra, Part 1-American Mathematical Society (2017) 1

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 Gröbner bases. Cover......Page 1 Title page......Page 4 Dedication......Page 6 Contents......Page 8 Preface to the third edition: Volume I......Page 12 Part A. Course I......Page 16 Chapter A-1. Classical formulas......Page 18 Chapter A-2. Classical number theory......Page 24 Chapter A-3. Commutative rings......Page 44 Chapter A-4. Groups......Page 130 Chapter A-5. Galois theory......Page 194 Chapter A-6. Appendix: Set theory......Page 250 Chapter A-7. Appendix: Linear Algebra......Page 262 Part B. Course II......Page 286 Chapter B-1. Modules......Page 288 Chapter B-2. Zorn’s lemma......Page 328 Chapter B-3. Advanced linear algebra......Page 374 Chapter B-4. Categories of modules......Page 456 Chapter B-5. Multilinear algebra......Page 558 Chapter B-6. Commutative algebra II......Page 606 Chapter B-7. Appendix: Categorical limits......Page 666 Chapter B-8. Appendix: Topological spaces......Page 688 Bibliography......Page 696 Special notation......Page 702 Index......Page 708 Back Cover......Page 722 Joseph J. Rotman. Includes Bibliographical References And Index.