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Abstract algebra : structures and applications

Author: Stephen Lovett
Publisher: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2016]
Edition/Format:   Print book : EnglishView all editions and formats

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Genre/Form: Textbooks
Document Type: Book
All Authors / Contributors: Stephen Lovett
ISBN: 9781482248906 1482248905
OCLC Number: 903812715
Notes: "A Chapman & Hall book."
Description: xii, 708 pages : illustrations ; 29 cm
Contents: SET THEORY Sets and Functions The Cartesian Product; Operations; Relations Equivalence Relations Partial Orders NUMBER THEORY Basic Properties of Integers Modular Arithmetic Mathematical Induction GROUPS Symmetries of the Regular n-gon Introduction to Groups Properties of Group Elements Symmetric Groups Subgroups Lattice of Subgroups Group Homomorphisms Group Presentations Groups in Geometry Diffie-Hellman Public Key Semigroups and Monoids QUOTIENT GROUPS Cosets and Lagrange's Theorem Conjugacy and Normal Subgroups Quotient Groups Isomorphism Theorems Fundamental Theorem of Finitely Generated Abelian Groups RINGS Introduction to Rings Rings Generated by Elements Matrix Rings Ring Homomorphisms Ideals Quotient Rings Maximal and Prime Ideals DIVISIBILITY IN COMMUTATIVE RINGS Divisibility in Commutative Rings Rings of Fractions Euclidean Domains Unique Factorization Domains Factorization of Polynomials RSA Cryptography Algebraic Integers FIELD EXTENSIONS Introduction to Field Extensions Algebraic Extensions Solving Cubic and Quartic Equations Constructible Numbers Cyclotomic Extensions Splitting Fields and Algebraic Closures Finite Fields GROUP ACTIONS Introduction to Group Actions Orbits and Stabilizers Transitive Group Actions Groups Acting on Themselves Sylow's Theorem A Brief Introduction to Representations of Groups CLASSIFICATION OF GROUPS Composition Series and Solvable Groups Finite Simple Groups Semidirect Product. Classification Theorems Nilpotent Groups MODULES AND ALGEBRAS Boolean Algebras Vector Spaces Introduction to Modules Homomorphisms and Quotient Modules Free Modules and Module Decomposition Finitely Generated Modules over PIDs, I Finitely Generated Modules over PIDs, II Applications to Linear Transformations Jordan Canonical Form Applications of the Jordan Canonical Form A Brief Introduction to Path Algebras GALOIS THEORY Automorphisms of Field Extensions Fundamental Theorem of Galois Theory First Applications of Galois Theory Galois Groups of Cyclotomic Extensions Symmetries among Roots; The Discriminant Computing Galois Groups of Polynomials Fields of Finite Characteristic Solvability by Radicals MULTIVARIABLE POLYNOMIAL RINGS Introduction to Noetherian Rings Multivariable Polynomial Rings and Affine Space The Nullstellensatz Polynomial Division; Monomial Orders Grobner Bases Buchberger's Algorithm Applications of Grobner Bases A Brief Introduction to Algebraic Geometry CATEGORIES Introduction to Categories Functors APPENDICES LIST OF NOTATIONS BIBLIOGRAPHY INDEX Projects appear at the end of each chapter.
Responsibility: Stephen Lovett, Wheaton College, Wheaton, Illinois, USA.


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"... lucid, detailed, and versatile main text comes with a wealth of illustrating examples and very instructive exercises in each single section of the book, and each chapter ends with a section Read more...

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