A first course in abstract algebra : rings, groups and fields /: rings, groups and fields. (2014)

• Record Type: Book
• Further Information: Note: Marlow Anderson and Todd Feil.
• Authors: Anderson, Marlow, 1950-; Feil, Todd, 1951-
• Contents: Numbers, Polynomials, and Factoring; The Natural Numbers; The Integers; Modular Arithmetic; Polynomials with Rational Coefficients; Factorization of Polynomials; Section I in a Nutshell Rings, Domains, and Fields; Rings; Subrings and Unity; Integral Domains and Fields; Ideals; Polynomials over a Field; Section II in a Nutshell Ring Homomorphisms and Ideals; Ring Homomorphisms; The Kernel; Rings of Cosets; The Isomorphism Theorem for Rings; Maximal and Prime Ideals; The Chinese Remainder Theorem; Section III in a Nutshell Groups; Symmetries of Geometric Figures; Permutations; Abstract Groups; Subgroups; Cyclic Groups; Section IV in a Nutshell Group Homomorphisms; Group Homomorphisms; Structure and Representation; Cosets and Lagrange's Theorem; Groups of Cosets; The Isomorphism Theorem for Groups; Section V in a Nutshell Topics from Group Theory ; The Alternating Groups; Sylow Theory: The Preliminaries; Sylow Theory: The Theorems; Solvable Groups; Section VI in a Nutshell Unique Factorization ; Quadratic Extensions of the Integers; Factorization; Unique Factorization; Polynomials with Integer Coefficients; Euclidean Domains; Section VII in a Nutshell Constructibility Problems; Constructions with Compass and Straightedge; Constructibility and Quadratic Field Extensions; The Impossibility of Certain Constructions; Section VIII in a Nutshell Vector Spaces and Field Extensions; Vector Spaces I; Vector Spaces II; Field Extensions and Kronecker's Theorem; Algebraic Field Extensions; Finite Extensions and Constructibility Revisited; Section IX in a Nutshell Galois Theory; The Splitting Field; Finite Fields; Galois Groups; The Fundamental Theorem of Galois Theory; Solving Polynomials by Radicals; Section X in a Nutshell Hints and Solutions Guide to Notation Index
• Edition: Third edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2014
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 512.02; Algebra, Abstract
• Languages: English
• ISBNs: 9781482245554; 9781482245530; 9781482245547
• Related ISBNs: 9781482245523
• 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.