Concepts in Abstract Algebra

ISBN-10: 053442323X

ISBN-13: 9780534423230

Edition: 2005

Authors: Charles Lanski

List price: $173.95
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Description:

Learn abstract algebra the easy way with CONCEPTS IN ABSTRACT ALGEBRA! This mathematics text shows you how mathematics proceeds, how to use techniques that mathematicians actually employ, and the art of constructing mathematical arguments. Extensive discussions, examples, repetition, development in nontrivial contexts, and exercises help you learn definitions and results. Examples show you how elementary material is developed and give you a template for writing your own arguments.
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Book details

List price: $173.95
Copyright year: 2005
Publisher: Brooks/Cole
Binding: Hardcover
Pages: 545
Size: 6.50" wide x 9.25" long x 1.00" tall
Weight: 1.936
Language: English

Review
Sets
Index Sets and Partitions
Induction I
Well Ordering and Induction II
Functions
Bijections and Inverses
Cardinality and Infinite Sets
Preliminaries
Remainders
Divisibility
Relative Primeness
Prime Factorization
Relations
Equivalence Relations
Congruence Modulo n
The Ring of Integers Mod n
Localization
Groups
Basic Notions and Examples
Uniqueness Properties
Groups of Symmetries
Orders of Elements
Subgroups
Special Subgroups
Special Groups
Cyclic Groups
The Groups U[subscript n]
The Symmetric Groups S[subscript n]
The Dihedral Groups D[subscript n]
Direct Sums
Subgroups
Cosets
Lagrange's Theorem and Consequences
Products of Subgroups
Products in Abelian Groups
Cauchy's Theorem and Cyclic Groups
The Groups U[subscript p superscript n] Are Cyclic
Carmichael Numbers
Encryption and Codes
Normal Subgroups and Quotients
Normal Subgroups
Quotient Groups
Some Results Using Quotient Groups
Simple Groups
Morphisms
Homomorphisms
Basic Results
The First Isomorphism Theorem
Applications
Automorphisms
Structure Theorems
The Correspondence Theorem
Two Isomorphism Theorems
Direct Sum Decompositions
Groups of Small Order
The Fundamental Theorem of Finite Abelian Groups
Conjugation
Conjugates
Conjugates and Centralizers in S[subscript n]
p-Groups
Sylow Subgroups
Group Actions
Group Actions
Counting Orbits
Sylow's Theorems
Applications of Sylow's Theorems
Rings
Definitions and Examples
Subrings
Polynomial and Related Rings
Zero Divisors and Domains
Indeterminates as Functions
Ideals, Quotients, and Homomorphisms
Ideals
Quotient Rings
Homomorphisms of Rings
Isomorphism Theorems
The Correspondence Theorem
Chain Conditions
Factorization in Integral Domains
Primes and Irreducibles
PIDs
UFDs
Euclidean Domains
Commutative Rings
Maximal and Prime Ideals
Localization Revisited
Noetherian Rings
Integrality
Algebraic Geometry
Zorn's Lemma and Cardinality
Fields
Vector Spaces
Subfields
Geometric Constructions
Splitting Fields
Algebraic Closures
Transcendental Extensions
Galois Theory
The Galois Correspondence
The Fundamental Theorem
Applications
Cyclotomic Extensions
Solvable Groups
Radical Extensions
Hints to Selected Odd-Numbered Problems
Index
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