Abstract algebra / Chih-han Sah.
Series Academic Press textbooks in mathematicsEditor: New York : Academic Press, c1967Descripción: xiii, 342 p. ; 24 cmTema(s): Algebra, AbstractOtra clasificación: 00A05CHAPTER 0 * PRELIMINARIES CHAPTER I CHAPTER II 0'1 Set Theoretic Notations [1] 0 • 2 Correspondences, Maps, Relations [2] 0 • 3 Cartesian Product and Universal Mapping Properties [8] 0 • 4 Cardinal Numbers [10] 0 • 5 Zorn’s Lemma, Axiom of Choice, Well-Ordering Axiom [12] References [15] • NATURAL NUMBERS, INTEGERS, AND RATIONAL NUMBERS I • 7 Peano’s Axioms [16] I • 2 Addition in P [22] I • 3 Ordering in P: A Second Definition in Finiteness [23] I • 4 Multiplication in P [27] I • 5 Construction of the Integers Z [28] I • 6 Divisibility Theory in Z [30] I • 7 Construction of the Rational Numbers Q [37] References [39] • GROUPS, RINGS, INTEGRAL DOMAINS, FIELDS 77 • 1 Multiplicative Systems: Groups [40] II • 2 Homomorphisms [44] II ’ 3 Rings, Integral Domains, and Fields [50] II • 4 Polynomial Rings 56 References [60] CHAPTER III - ELEMENTARY THEORY OF GROUPS III • 1 Basic Concepts [62] III • 2 Homomorphisms of Groups [68] III • 3 Transformation Groups: Sy low’s Theorem [73] III • 4 The Finite Symmetric Groups Sn [80] III • 5 Direct Product of Groups: Fundamental Theorem of Finite Abelian Groups [89] References [98] CHAPTER IV • ELEMENTARY THEORY OF RINGS IV •1 Basic Concepts [101] IV • 2 Divisibility Theory in Integral Domains [105] IV • 3 Fields of Rational Functions: Partial Fraction Decomposition [120] IV • 4 Modules and Their Endomorphism Rings. Matrices [122] IV - 5 Rings of Functions [137] References [139] CHAPTER V ■ MODULES AND ASSOCIATED ALGEBRAS OVER COMMUTATIVE RINGS V • 1 Tensor Product of Modules over Commutative Rings [142] V • 2 Free Modules over a PID [147] V • 3 Modules of Finite Type over a PID [160] V * 4 Tensor Algebras, Exterior Algebras, and Determinants [172] V • 5 Derivations, Traces, and Characteristic Polynomials [188] V • 6 Dual Modules 196 References [208] CHAPTER VI * VECTOR SPACES VI • 1 Basic Concepts [210] VI • 2 Systems of Linear Equations [220] VI • 3 Decomposition of a Vector Space with Respect to a Linear Endomorphism [223] VI • 4 Canonical Forms of Matrices: Characteristic Values: Characteristic Vectors 232 References [237] CHAPTIR VII • ELEMENTARY THEORY OF FIELDS VII • 1 Basic Concepts [240] VII• 2 Algebraic Extension Fields: Splitting Fields [246] VII • 3 Algebraically Closed Fields: Algebraic Closure [251] VII • 4 Algebraic Independence: Purely Transcendental Extensions: Transcendence Base [256] VII * 5 Separable and Inseparable Algebraic Field Extensions [263] VII • 6 Finite Fields: Primitive Element Theorem [276] References [283] CHAPTIR VIII * GALOIS THIORY VIII' I Basic Concepts [286] VIII • 2 Fundamental Theorems [294] VIII • 3 Solvability of Polynomial Equations by Radicals [305] VIII • 4 Cyclotomic Polynomials over Q: Kummer Extensions 313 References [318] CHAPTER IX * REAL AND COMPLEX NUMBERS IX * 1 Construction of Real and Complex Numbers [320] IX • 2 Fundamental Theorem of Algebra [328] References [333] Subject Index [335]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
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Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A Sa131 (Browse shelf) | Available | A-4305 |
Incluye referencias bibliográficas.
CHAPTER 0 * PRELIMINARIES --
CHAPTER I --
CHAPTER II --
0'1 Set Theoretic Notations [1] --
0 • 2 Correspondences, Maps, Relations [2] --
0 • 3 Cartesian Product and Universal Mapping Properties [8] --
0 • 4 Cardinal Numbers [10] --
0 • 5 Zorn’s Lemma, Axiom of Choice, Well-Ordering Axiom [12] --
References [15] --
• NATURAL NUMBERS, INTEGERS, AND RATIONAL NUMBERS --
I • 7 Peano’s Axioms [16] --
I • 2 Addition in P [22] --
I • 3 Ordering in P: A Second Definition in Finiteness [23] --
I • 4 Multiplication in P [27] --
I • 5 Construction of the Integers Z [28] --
I • 6 Divisibility Theory in Z [30] --
I • 7 Construction of the Rational Numbers Q [37] --
References [39] --
• GROUPS, RINGS, INTEGRAL DOMAINS, FIELDS --
77 • 1 Multiplicative Systems: Groups [40] --
II • 2 Homomorphisms [44] --
II ’ 3 Rings, Integral Domains, and Fields [50] --
II • 4 Polynomial Rings 56 References [60] --
CHAPTER III - ELEMENTARY THEORY OF GROUPS --
III • 1 Basic Concepts [62] --
III • 2 Homomorphisms of Groups [68] --
III • 3 Transformation Groups: Sy low’s Theorem [73] --
III • 4 The Finite Symmetric Groups Sn [80] --
III • 5 Direct Product of Groups: Fundamental Theorem of Finite Abelian Groups [89] --
References [98] --
CHAPTER IV • ELEMENTARY THEORY OF RINGS --
IV •1 Basic Concepts [101] --
IV • 2 Divisibility Theory in Integral Domains [105] --
IV • 3 Fields of Rational Functions: Partial Fraction Decomposition [120] --
IV • 4 Modules and Their Endomorphism Rings. Matrices [122] --
IV - 5 Rings of Functions [137] --
References [139] --
CHAPTER V ■ MODULES AND ASSOCIATED ALGEBRAS OVER COMMUTATIVE RINGS --
V • 1 Tensor Product of Modules over Commutative Rings [142] --
V • 2 Free Modules over a PID [147] --
V • 3 Modules of Finite Type over a PID [160] --
V * 4 Tensor Algebras, Exterior Algebras, and Determinants [172] --
V • 5 Derivations, Traces, and Characteristic Polynomials [188] --
V • 6 Dual Modules 196 References [208] --
CHAPTER VI * VECTOR SPACES --
VI • 1 Basic Concepts [210] --
VI • 2 Systems of Linear Equations [220] --
VI • 3 Decomposition of a Vector Space with Respect to a Linear Endomorphism [223] --
VI • 4 Canonical Forms of Matrices: Characteristic Values: Characteristic Vectors 232 References [237] --
CHAPTIR VII • ELEMENTARY THEORY OF FIELDS --
VII • 1 Basic Concepts [240] --
VII• 2 Algebraic Extension Fields: Splitting Fields [246] --
VII • 3 Algebraically Closed Fields: Algebraic Closure [251] --
VII • 4 Algebraic Independence: Purely Transcendental Extensions: Transcendence Base [256] --
VII * 5 Separable and Inseparable Algebraic Field Extensions [263] --
VII • 6 Finite Fields: Primitive Element Theorem [276] --
References [283] --
CHAPTIR VIII * GALOIS THIORY --
VIII' I Basic Concepts [286] --
VIII • 2 Fundamental Theorems [294] --
VIII • 3 Solvability of Polynomial Equations by Radicals [305] --
VIII • 4 Cyclotomic Polynomials over Q: Kummer Extensions 313 References [318] --
CHAPTER IX * REAL AND COMPLEX NUMBERS --
IX * 1 Construction of Real and Complex Numbers [320] --
IX • 2 Fundamental Theorem of Algebra [328] --
References [333] --
Subject Index [335] --
MR, 36 #6245
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