Concepts in Abstract Algebra

Name: Concepts in Abstract Algebra
Price: 146.02 USD
Availability: InStock
ISBN: 9780534423230

ISBN-10: 053442323X

ISBN-13: 9780534423230

Edition: 2005

Authors: Charles Lanski

List price: $173.95

30 day, 100% satisfaction guarantee!

Marketplace

1 new & used from $146.02

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

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.

Book details

List price: $173.95
Copyright year: 2005
Publisher: American Mathematical Society
Publication date: 9/30/2004
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