Autorentext

Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.

Klappentext

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.

Inhalt

• 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