Introduction to abstract algebra. (2015)

• Record Type: Book
• Further Information: Note: Jonathan D.H. Smith.
• Authors: Smith, Jonathan D. H, 1949-
• Contents: Numbers; Ordering numbers; The Well-Ordering Principle; Divisibility; The Division Algorithm; Greatest common divisors; The Euclidean Algorithm; Primes and irreducibles; The Fundamental Theorem of Arithmetic; Exercises; Study projects; Notes; ; Functions; Specifying functions; Composite functions; Linear functions; Semigroups of functions; Injectivity and surjectivity; Isomorphisms; Groups of permutations; Exercises; Study projects; Notes; Summary; ; Equivalence; Kernel and equivalence relations; Equivalence classes; Rational numbers; The First Isomorphism Theorem for Sets; Modular arithmetic; Exercises; Study projects; Notes; ; Groups and Monoids; Semigroups; Monoids; Groups; Componentwise structure; Powers; Submonoids and subgroups; Cosets; Multiplication tables; Exercises; Study projects; Notes; ; Homomorphisms ; Homomorphisms; Normal subgroups; Quotients; The First Isomorphism Theorem for Groups; The Law of Exponents; Cayley’s Theorem; Exercises; Study projects; Notes; ; Rings; Rings; Distributivity; Subrings; Ring homomorphisms; Ideals; Quotient rings; Polynomial rings; Substitution; Exercises; Study projects; Notes; ; Fields; Integral domains; Degrees; Fields; Polynomials over fields; Principal ideal domains; Irreducible polynomials; Lagrange interpolation; Fields of fractions; Exercises; Study projects; Notes; ; Factorization; Factorization in integral domains; Noetherian domains; Unique factorization domains; Roots of polynomials; Splitting fields; Uniqueness of splitting fields; Structure of finite fields; Galois fields; Exercises; Study projects; Notes; ; Modules; Endomorphisms; Representing a ring ; Modules; Submodules; Direct sums; Free modules; Vector spaces; Abelian groups; Exercises; Study projects; Notes; ; Group Actions; Actions; Orbits; Transitive actions; Fixed points; Faithful actions; Cores; Alternating groups; Sylow Theorems; Exercises; Study projects; Notes; ; Quasigroups; Quasigroups; Latin squares; Division; Quasigroup homomorphisms; Quasigroup homotopies; Principal isotopy; Loops; Exercises; Study projects; Note; ; Index
• Edition: Second edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.02; Algebra, Abstract
• Languages: English
• ISBNs: 9781498731812; 9781498731621; 9781498731805
• Related ISBNs: 9781498731614
• Notes: 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.