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Informationen zum Autor David S. Dummit and Richard M. Foote are the authors of Abstract Algebra, 3rd Edition, published by Wiley. Klappentext Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. The book carefully develops the theory of different algebraic structures, beginning from basic definitions to some in-depth results, using numerous examples and exercises to aid the reader's understanding. In this way, readers gain an appreciation for how mathematical structures and their interplay lead to powerful results and insights in a number of different settings.* The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible. Zusammenfassung Widely acclaimed algebra text. This book is designed to give the reader insight into the power and beauty that accrues from a rich interplay between different areas of mathematics. Inhaltsverzeichnis Preface. Preliminaries. PART I: GROUP THEORY. Chapter 1. Introduction to Groups. Chapter 2. Subgroups. Chapter 3. Quotient Group and Homomorphisms. Chapter 4. Group Actions. Chapter 5. Direct and Semidirect Products and Abelian Groups. Chapter 6. Further Topics in Group Theory. PART II: RING THEORY. Chapter 7. Introduction to Rings. Chapter 8. Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains. Chapter 9. Polynomial Rings. PART III: MODULES AND VECTOR SPACES. Chapter 10. Introduction to Module Theory. Chapter 11. Vector Spaces. Chapter 12. Modules over Principal Ideal Domains. PART IV: FIELD THEORY AND GALOIS THEORY. Chapter 13. Field Theory. Chapter 14. Galois Theory. PART V: AN INTRODUCTION TO COMMUTATIVE RINGS, ALGEBRAIC GEOMETRY, AND HOMOLOGICAL ALGEBRA. Chapter 15. Commutative Rings and Algebraic Geometry. Chapter 16. Artinian Rings, Discrete Valuation Rings, and Dedekind Domains. Chapter 17. Introduction to Homological Algebra and Group Cohomology. PART VI: INTRODUCTION TO THE REPRESENTATION THEORY OF FINITE GROUPS. Chapter 18. Representation Theory and Character Theory. Chapter 19. Examples and Applications of Character Theory. Appendix I: Cartesian Products and Zorn's Lemma. Appendix II: Category Theory. Index. ...
Sommario
Preliminaries
Part I Group Theory
* Introduction to Groups
* Subgroups
* Quotient Groups and Homomorphisms
* Group Actions
* Direct and Semidirect Products and Abelian Groups
* Further Topics in Group Theory
Part II Ring Theory
* Introduction to Rings
* Euclidean Domains, Principal Ideal Domains and Unique Factorization Domains
* Polynomial Rings
Part III Modules and Vector Spaces
* Introduction to Module Theory
* Vector Spaces
* Modules over Principal Ideal Domains
Part IV Field Theory and Galois Theory
* Field Theory
* Galois Theory
Part V An Introduction To Commutative Rings, Algabraic Geometry, and Homological Algebra
* Commutative Rings and Algebraic Geometry
* Artinian Rings, Discrete Valuation Rings, and Dedekind Domains
* Introduction to Homological Algebra and Group Cohomology
Part IV Introduction To The Representation Theory of Finite Groups
* Representation Theory and Character Theory
* Examples and Applications of Character Theory
Appendix I Cartesian Products and Zorn's Lemma
Appendix II Category Theory Index
