Introduction to Abstract Algebra
Published on 7. July 2022
184 pages
978-2-7598-2916-3 (ISBN)
Description
No detailed description available for "Introduction to Abstract Algebra".
More details
Series
Edition
Digital original
Language
English
Place of publication
Les Ulis
France
Target group
Professional and scholarly
US School Grade: College Graduate Student
Edition type
Digital original
ISBN-13
978-2-7598-2916-3 (9782759829163)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Persons
Li Libin:
Libin LI is professor at School of Mathematics,Yangzhou University in China. His research interests include Representation theoryin Hopf algebras and Tensor category, Decoding theory and Ring theory, Weylalgebras and isomorphism problems, etc.Zhao Kaiming:
Kaiming ZHAO conducts teaching and research in thefields of Lie algebra, Representation theory, Associative Algebra, Linear Algebra,and Division Algebra. He is professor in Wilfrid Laurier University, Canadasince 2009.
Libin LI is professor at School of Mathematics,Yangzhou University in China. His research interests include Representation theoryin Hopf algebras and Tensor category, Decoding theory and Ring theory, Weylalgebras and isomorphism problems, etc.Zhao Kaiming:
Kaiming ZHAO conducts teaching and research in thefields of Lie algebra, Representation theory, Associative Algebra, Linear Algebra,and Division Algebra. He is professor in Wilfrid Laurier University, Canadasince 2009.
Content
- Cover-1
- Cover-2
- Introduction to Abstract Algebra
- Preface
- Contents
- Notations
- Chapter 1 Groups and Generating Sets
- 1.1 Binary operations
- 1.2 Isomorphic binary structures
- 1.3 Groups
- 1.4 Subgroups
- 1.5 Cyclic groups
- 1.6 Generating sets
- 1.7 Exercises
- Chapter 2 Permutation Groups and Alternating Groups
- 2.1 Permutation groups
- 2.2 Alternating groups
- 2.3 Exercises
- Chapter 3 Finitely Generated Abelian Groups and Quotient Groups
- 3.1 The theorem of Lagrange
- 3.2 Finitely generated abelian groups
- 3.3 Properties of homomorphisms
- 3.4 Quotient groups and isomorphism theorems
- 3.5 Automorphism groups
- 3.6 Simple groups
- 3.7 Exercises
- Chapter 4 Rings, Quotient Rings and Ideal Theory
- 4.1 Basic definitions
- 4.2 Integral domains
- 4.3 Noncommutative rings
- 4.4 Quaternions
- 4.5 Isomorphism theorems
- 4.6 Euler's theorem
- 4.7 Ideal theory
- 4.8 Exercises
- Chapter 5 Unique Factorization Domains
- 5.1 Basic definitions
- 5.2 Principal ideal domains
- 5.3 Euclidean domains
- 5.4 Polynomial rings over UFDs
- 5.5 Multiplicative norms
- 5.6 Exercises
- Chapter 6 Extension Fields
- 6.1 Prime fields and extension fields
- 6.2 Algebraic and transcendental elements
- 6.3 Algebraic extensions and algebraic closure
- 6.4 Finite fields
- 6.5 Exercises
- Appendix A Equivalence Relations and Quotient Set
- Appendix B Zorn's Lemma
- Appendix C Quotient field
- Reference
- Index
