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CONCEPTS IN ABSTRACT ALGEBRA (BROOKS/COLE SERIES IN By Charles Lanski EXCELLENT
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Located in: Gatlinburg, Tennessee, United States
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eBay item number:315211049217
Item specifics
- Condition
- Like New
- Seller notes
- “Looks new”
- ISBN-10
- 053442323X
- Book Title
- Concepts in Abstract Algebra (Brooks/Cole Series in Advanced
- ISBN
- 9780534423230
- Subject Area
- Mathematics
- Publication Name
- concepts in Abstract Algebra
- Publisher
- American Mathematical Society
- Item Length
- 9.4 in
- Subject
- Algebra / Abstract
- Publication Year
- 2004
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 1 in
- Item Weight
- 31.4 Oz
- Item Width
- 6.6 in
- Number of Pages
- 545 Pages
About this product
Product Information
Helps students learn the core concepts and associated techniques in algebra. This book offers exercises that require the use and synthesis of the techniques and results. It also helps students learn the art of constructing mathematical arguments.
Product Identifiers
Publisher
American Mathematical Society
ISBN-10
053442323x
ISBN-13
9780534423230
eBay Product ID (ePID)
23038753435
Product Key Features
Number of Pages
545 Pages
Language
English
Publication Name
concepts in Abstract Algebra
Publication Year
2004
Subject
Algebra / Abstract
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
1 in
Item Weight
31.4 Oz
Item Length
9.4 in
Item Width
6.6 in
Additional Product Features
LCCN
2004-105799
Dewey Edition
22
Target Audience
Scholarly & Professional
Illustrated
Yes
Dewey Decimal
512/.02
Lc Classification Number
Qa162.L36 2005
Table of Content
0. REVIEW. Sets. Index Sets and Partitions. Induction. Well Ordering and Induction. Functions. Bijections and Inverses. Cardinality and Infinite Sets. 1. PRELIMINARIES. Remainders. Divisibility. Relative Primeness. Prime Factorization. Relations. Equivalence Relations. Congruence Modulo n. The Ring of Integers Mod n. Localization. 2. GROUPS. Basic Notions and Examples. Uniqueness Properties. Groups of Symmetries. Orders of Elements. Subgroups. Special Subgroups. 3. SPECIAL GROUPS. Cyclic Groups. The Groups Un. The Symmetric Groups Sn. The Dihedral Groups Dn. Direct Sums. 4. SUBGROUPS. Cosets. Lagrange's Theorem and Consequences. Products of Subgroups. Products in Abelian Groups. Cauchy's Theorem and Cyclic Groups. The Groups Up are Cyclic. Carmichael Numbers. Encryption and Codes. 5. NORMAL SUBGROUPS AND QUOTIENTS. Normal Subgroups. Quotient Groups. Some Results Using Quotient Groups. Simple Groups. 6. MORPHISMS. Homomorphisms. Basic Results. The First Isomorphism Theorem. Applications. Automorphisms. 7. STRUCTURE THEOREMS. The Correspondence Theorem. Two Isomorphism Theorems. Direct Sum Decompositions. Groups of Small Order. Fundamental Theorem of Finite Abelian Groups. 8. CONJUGATION. Conjugates. Conjugates and Centralizers in Sn. p-Groups. Sylow Subgroups. 9. GROUP ACTIONS. Group Actions. Counting Orbits. Sylow's Theorems. Applications of Sylow's Theorems. 10. RINGS. Definitions and Examples. Subrings. Polynomial and Related Rings. Zero Divisors and Domains. Indeterminates as Functions. 11. IDEALS, QUOTIENTS, AND HOMOMORPHISMS. Ideals. Quotient Rings. Homomorphisms of Rings. Isomorphism Theorems. The Correspondence Theorem. Chain Conditions. 12. FACTORIZATION IN INTEGRAL DOMAINS. Primes and Irreducibles. PIDs. UFDs. Euclidean Domains. 13. COMMUTATIVE RINGS. Maximal and Prime Ideals. Localization Revisited. Noetherian Rings. Integrality. Algebraic Geometry. Zorn's Lemma and Cardinality. 14. FIELDS. Vector Spaces. Subfields. Geometric Constructions. Splitting Fields. Algebraic Closures. Transcendental Extensions. 15. GALOIS THEORY. The Galois Correspondence. The Fundamental Theorem. Applications. Cyclotomic Extensions. Solvable Groups. Radical Extensions. Hints to Selected Odd Numbered Problems. Index.
Copyright Date
2005
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