An Introduction to Algebraic Structures
by Landin, JosephEdition: Reprint
Format: Paperback
Pub. Date: 2010-10-18
Publisher(s): Dover Publications
Other versions by this Author
List Price: $17.23
Buy New
Usually Ships in 5-7 Business Days
$16.41
Rent Textbook
Select for Price
Digital
$17.94*
Used Textbook
We're Sorry
Sold Out
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
Superb, self-contained text covers sets and numbers, the elements of set theory, the real numbers, the theory of groups, group isomorphism and homomorphism, the theory of rings, and polynomial rings. Numerous examples and exercises. Ideal for one-semester course. 1969 edition.
Author Biography
A Professor Emeritus at the University of Illinois, Joseph Landin served as Head of the Department of Mathematics for 10 years.
Table of Contents
1. Sets and Numbers
I. THE ELEMENTS OF SET THEORY
1. The Concept of Set
2. "Constants, Variables and Related Matters"
3. Subsets and Equality of Sets
4. The Algebra of Sets; The Empty Set
5. A Notation for Sets
6. Generalized Intersection and Union
7. Ordered Pairs and Cartesian Products
8. Functions (or Mappings)
9. A Classification of Mappings
10. Composition of Mappings
11. Equivalence Relations and Partititions
II. THE REAL NUMBERS
12. Introduction
13. The Real Numbers
14. The Natural Numbers
15. The Integers
16. The Rational Numbers
17. The Complex Numbers
2. The Theory of Groups
1. The Group Concept
2. Some Simple Consequences of the Definition of Group
3. Powers of Elements in a Group
4. Order of a Group; Order of a Group Element
5. Cyclic Groups
6. The Symmetric Groups
7. Cycles; Decomposition of Permutations into Disjoint Cycles
8. Full Transformation Groups
9. Restrictions of Binary Operations
10. Subgroups
11. A Discussion of Subgroups
12. The Alternating Group
13. The Congruence of Integers
14. The Modular Arithmetics
15. Equivalence Relations and Subgroups
16. Index of a Subgroup
17. "Stable Relations, Normal Subgroups, Quotient Groups"
18. Conclusion
3. Group Isomorphism and Homomorphism
1. Introduction
2. "Group Isomorphism; Examples, Definitions and Simplest Properties"
3. The Isomorphism Theorem for the Symmetric Groups
4. The Theorem of Cayley
5. Group Homomorphisms
6. A Relation Between Epimorphisms and Isomorphisms
7. Endomorphisms of a Group
4. The Theory of Rings
1. Introduction
2. Definition of Ring
3. Some Properties of Rings
4. "The Modular Arithmetics, Again"
5. Integral Domains
6. Fields
7. Subrings
8. Ring Homomorphisms
9. Ideals
10. Residue Class Rings
11. Some Basic Homomorphism Theorems
12. Principle Ideal and Unique Factorization Domains
13. Prime and Maximal Ideals
14. The Quotient Field of an Integral Domain
5. Polynomial Rings
1. Introduction; The Concept of Polynomial Ring
2. Indeterminates
3. Existence of Indeterminates
4. Polynomial Domains Over a Field
5. Unique Factorization in Polynomial Domains
6. Polynomial Rings in Two Indeterminates
7. Polynomial Functions and Polynomials
8. Some Characterizations of Intermediates
9. Substitution Homomorphisms
10. Roots of Polynomials
I. THE ELEMENTS OF SET THEORY
1. The Concept of Set
2. "Constants, Variables and Related Matters"
3. Subsets and Equality of Sets
4. The Algebra of Sets; The Empty Set
5. A Notation for Sets
6. Generalized Intersection and Union
7. Ordered Pairs and Cartesian Products
8. Functions (or Mappings)
9. A Classification of Mappings
10. Composition of Mappings
11. Equivalence Relations and Partititions
II. THE REAL NUMBERS
12. Introduction
13. The Real Numbers
14. The Natural Numbers
15. The Integers
16. The Rational Numbers
17. The Complex Numbers
2. The Theory of Groups
1. The Group Concept
2. Some Simple Consequences of the Definition of Group
3. Powers of Elements in a Group
4. Order of a Group; Order of a Group Element
5. Cyclic Groups
6. The Symmetric Groups
7. Cycles; Decomposition of Permutations into Disjoint Cycles
8. Full Transformation Groups
9. Restrictions of Binary Operations
10. Subgroups
11. A Discussion of Subgroups
12. The Alternating Group
13. The Congruence of Integers
14. The Modular Arithmetics
15. Equivalence Relations and Subgroups
16. Index of a Subgroup
17. "Stable Relations, Normal Subgroups, Quotient Groups"
18. Conclusion
3. Group Isomorphism and Homomorphism
1. Introduction
2. "Group Isomorphism; Examples, Definitions and Simplest Properties"
3. The Isomorphism Theorem for the Symmetric Groups
4. The Theorem of Cayley
5. Group Homomorphisms
6. A Relation Between Epimorphisms and Isomorphisms
7. Endomorphisms of a Group
4. The Theory of Rings
1. Introduction
2. Definition of Ring
3. Some Properties of Rings
4. "The Modular Arithmetics, Again"
5. Integral Domains
6. Fields
7. Subrings
8. Ring Homomorphisms
9. Ideals
10. Residue Class Rings
11. Some Basic Homomorphism Theorems
12. Principle Ideal and Unique Factorization Domains
13. Prime and Maximal Ideals
14. The Quotient Field of an Integral Domain
5. Polynomial Rings
1. Introduction; The Concept of Polynomial Ring
2. Indeterminates
3. Existence of Indeterminates
4. Polynomial Domains Over a Field
5. Unique Factorization in Polynomial Domains
6. Polynomial Rings in Two Indeterminates
7. Polynomial Functions and Polynomials
8. Some Characterizations of Intermediates
9. Substitution Homomorphisms
10. Roots of Polynomials
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.