Advanced Modern Algebra
Third Edition, Parts 1 and 2
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-4174-6 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-4174-6 (ISBN)
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This new edition, now in two parts, has been significantly reorganised and many sections have been rewritten. The first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. The second part presents many topics mentioned in the first part in greater depth and in more detail.
This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The 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.
The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. The 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.
The second part presents many topics mentioned in the first part in greater depth and in more detail. The five chapters of the book are devoted to group theory, representation theory, homological algebra, categories, and commutative algebra, respectively. The book can be used as a text for a second abstract algebra graduate course, as a source of additional material to a first abstract algebra graduate course, or for self-study.
Joseph J. Rotman, University of Illinois at Urbana-Champaign, IL.
Contents for Part 1:
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
Contents for Part 2: More groups
Representation theory
Homology
More categories
Commutative rings III
Bibliography
Index.
| Erscheinungsdatum | 28.09.2017 |
|---|---|
| Reihe/Serie | Graduate Studies in Mathematics |
| Verlagsort | Providence |
| Sprache | englisch |
| Maße | 152 x 229 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 1-4704-4174-8 / 1470441748 |
| ISBN-13 | 978-1-4704-4174-6 / 9781470441746 |
| Zustand | Neuware |
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