First Course in Abstract Algebra : Rings, Groups, and Fields, Third Edition.
Numbers, Polynomials, and Factoring The Natural Numbers The Integers Modular Arithmetic Polynomials with Rational CoefficientsFactorization of PolynomialsSection I in a NutshellRings, Domains, and Fields Rings Subrings and Unity Integral Domains and Fields Ideals Polynomials over a Field Section II...
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| Format: | eBook |
| Language: | English |
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Oakville :
CRC Press,
2014.
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| Edition: | 3rd ed. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | Numbers, Polynomials, and Factoring The Natural Numbers The Integers Modular Arithmetic Polynomials with Rational CoefficientsFactorization of PolynomialsSection I in a NutshellRings, Domains, and Fields Rings Subrings and Unity Integral Domains and Fields Ideals Polynomials over a Field Section II in a NutshellRing Homomorphisms and Ideals Ring HomomorphismsThe Kernel Rings of Cosets The Isomorphism Theorem for Rings Maximal and Prime Ideals The Chinese Remainder Theorem Section III in a NutshellGroups Symmetries of Geometric Figures PermutationsAbstract Groups Subgroups Cyclic Groups Section IV in a NutshellGroup Homomorphisms Group Homomorphisms Structure and Representation Cosets and Lagrange's Theorem Groups of CosetsThe Isomorphism Theorem for Groups Section V in a NutshellTopics from Group Theory The Alternating Groups Sylow Theory: The Preliminaries Sylow Theory: The Theorems Solvable Groups Section VI in a NutshellUnique Factorization Quadratic Extensions of the Integers FactorizationUnique Factorization Polynomials with Integer Coefficients Euclidean Domains Section VII in a NutshellConstructibility Problems Constructions with Compass and Straightedge Constructibility and Quadratic Field Extensions The Impossibility of Certain Constructions Section VIII in a NutshellVector Spaces and Field Extensions Vector Spaces IVector Spaces II Field Extensions and Kronecker's Theorem Algebraic Field Extensions Finite Extensions and Constructibility Revisited Section IX in a NutshellGalois Theory The Splitting Field Finite Fields Galois Groups The Fundamental Theorem of Galois TheorySolving Polynomials by Radicals Section X in a Nutshell Hints and Solutions Guide to Notation Index. |
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| Item Description: | Description based upon print version of record. |
| Physical Description: | 1 online resource (547 pages) |
| ISBN: | 9781482245530 1482245531 |