Abstract algebra : structures and applications /: structures and applications. (2015)

• Record Type: Book
• Further Information: Note: Stephen Lovett.
• Authors: Lovett, Stephen (Stephen T.)
• 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; Gröbner Bases; Buchberger’s Algorithm; Applications of Gröbner 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.
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations
• Subjects: 512.02; Algebra, Abstract
• Languages: English
• ISBNs: 9781482248913; 9781482248920
• Related ISBNs: 9781482248906
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.