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. -

-This text refers to the Hardcover edition.

Part Ⅰ- GROUP THEORY
Chapter 1 Introduction to Groups
Chapter 2 Subgroups
Chapter 3 Quotient Groups 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 INTRODUCTON 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 Introdeuction to Homological Algebra and Group Cohomology
Part Ⅵ- INTRODUCTION TO THE REPRESENTATION THEORY OF NINITE4 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

David S. Dummit, Richard M. Foote

배송정보

교환/반품 정보