A first course in abstract algebra : rings, groups and fields /: rings, groups and fields. (2014)
- Record Type:
- Book
- Title:
- A first course in abstract algebra : rings, groups and fields /: rings, groups and fields. (2014)
- Main Title:
- A first course in abstract algebra : rings, groups and fields
- 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;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 … (more)
- 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.
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.144352
- Ingest File:
- 02_127.xml