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CONCEPTS IN ABSTRACT ALGEBRA (BROOKS/COLE SERIES IN By Charles Lanski EXCELLENT - Picture 1 of 1
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CONCEPTS IN ABSTRACT ALGEBRA (BROOKS/COLE SERIES IN By Charles Lanski EXCELLENT

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Condition
Like New
A book that has been read, but looks new. The book cover has no visible wear, and the dust jacket (if applicable) is included for hard covers. No missing or damaged pages, no creases or tears, no underlining or highlighting of text, and no writing in the margins. May have no identifying marks on the inside cover. No wear and tear. See the seller’s listing for full details and description of any imperfections. See all condition definitionsopens in a new window or tab
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ISBN-10
053442323X
Book Title
Concepts in Abstract Algebra (Brooks/Cole Series in Advanced
ISBN
9780534423230
Publication Year
2004
Type
Textbook
Format
Hardcover
Language
English
Publication Name
concepts in Abstract Algebra
Item Height
1in
Author
Not Available
Item Length
9.4in
Publisher
American Mathematical Society
Item Width
6.6in
Item Weight
31.4 Oz
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

Author
Not Available
Publication Name
concepts in Abstract Algebra
Format
Hardcover
Language
English
Publication Year
2004
Type
Textbook
Number of Pages
545 Pages

Dimensions

Item Length
9.4in
Item Height
1in
Item Width
6.6in
Item Weight
31.4 Oz

Additional Product Features

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
Target Audience
Scholarly & Professional
Topic
Algebra / Abstract
Lccn
2004-105799
Dewey Decimal
512/.02
Dewey Edition
22
Illustrated
Yes
Genre
Mathematics

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