Fundamental structures of algebra / George D. Mostow, Joseph H. Sampson, Jean-Pierre Meyer.
Editor: New York : McGraw-Hill, c1963Descripción: xvi, 585 p. : il. ; 25 cmTema(s): AlgebraOtra clasificación: 00A05Contents Preface v List of Special Symbols xv 1. Binary Operations and Groups [1] 1. INTRODUCTION [1] 2. SETS AND MAPPINGS [1] 3. BINARY OPERATIONS [5] 4. THE ASSOCIATIVE AXIOM [8] 5. THE COMMUTATIVE AXIOM [11] 6. GROUPS [12] 7. ISOMORPHISMS AND HOMOMORPHISMS [16] 8. RESTATEMENT OF THE GROUP AXIOMS [20] 9. SYSTEMS WITH TWO BINARY OPERATIONS: RINGS, INTEGRAL DOMAINS, FIELDS [21] 2. Rings, Integral Domains, the Integers [28] 1. INTRODUCTION [28] 2. SYSTEMS WITH TWO BINARY OPERATIONS: RINGS AND INTEGRAL DOMAINS [28] 3. ORDERED INTEGRAL DOMAINS [32] 4. THE SYSTEM OF INTEGERS [36] 5. SOME COMMENTS [39] 6. FINITE AND COUNTABLE SETS [42] 7. MATHEMATICAL INDUCTION AND SOME OF ITS APPLICATIONS [43] 8. SOME ELEMENTARY NUMBER THEORY [54] 9. NOTATION FOR INTEGERS [62] 10. MORE ELEMENTARY NUMBER THEORY: CONGRUENCES [66] 11. PROOF OF THEOREM 4.4 [77] 3. Fields, the Rational Numbers [81] 1. INTRODUCTION [81] 2. FIELDS [81] 3. THE FIELD OF RATIONAL NUMBERS [85] 4. DECIMALS [89] 5. THE BINOMIAL THEOREM [95] 4. The Real-number System [100] 1. INTRODUCTION [100] 2. CAUCHY SEQUENCES AND LIMITS [102] 3. THE FIELD OF REAL NUMBERS [100] 4. SOME PROPERTIES OF R [111] 5. The Field of Complex Numbers [118] 1. THE SQUARE ROOT OF -1 [118] 2. A CONSTRUCTION OF C; QUATERNIONS [122] 3. A GEOMETRIC INTERPRETATION OF ADDITION AND MULTIPLICATION OF COMPLEX NUMBERS [125] 4. CAUCHY SEQUENCES AND INFINITE SERIES IN C [129] 6. Polynomials [133] 1. INTRODUCTION [133] 2. INDETERMINATES, OR VARIABLES [133] 3. FACTORIZATION OF POLYNOMIALS [140] 4. ROOTS OF POLYNOMIALS [148] 5. POLYNOMIALS IN SEVERAL VARIABLES [153] 6. POLYNOMIALS OF DEGREE LESS THAN 5 [158] 7. Rational Functions [163] 1. INTRODUCTION [163] 2. RATIONAL FUNCTIONS [163] 3. PARTIAL FRACTIONS [165] 8. Vector Spaces and Affine Spaces [171] 1. INTRODUCTION [171] 2. THE BASIC DEFINITIONS [171] 3. SOME CONSEQUENCES OF THE AXIOMS [172] 4. SOME IMPORTANT EXAMPLES [174] 5. SUBSPACES [176] 9. LINEAR INDEPENDENCE AND DIMENSION [178] 7. A THEOREM ON LINEAR EQUATIONS [180] X ON THE DIMENSION OF VECTOR SPACES [182] 9. BASE VECTORS [183] 10. AFFINE SPACES [187] 11. EUCLIDEAN SPACES [198] 12. ANALYTIC GEOMETRY [205] 9. Linear Transformations and Matrices [216] 1. INTRODUCTION [216] 2. A NOTATIONAL CONVENTION [216] X LINEAR MAPPINGS [217] 4. OPERATIONS ON LINEAR MAPPINGS [221] 5. LINEAR TRANSFORMATIONS AND MATRICES [225] 9. OPERATIONS ON MATRICES [231] 7. CHANGE OF BASE [238] 8. RANK OF A MATRIX; LINEAR EQUATIONS; SUBSPACES [242] 9. REDUCTION TO DIAGONAL FORM [249] 10. QUOTIENT SPACES [258] 11 MODULES [261] 10. Groups and Permutations [266] 1. INTRODUCTION [266] 2. BASIC PROPERTIES [266] 3. PERMUTATIONS [268] 4. SUBGROUPS AND QUOTIENT GROUPS [275] S. TRANSFORMATION GROUPS; SYLOW'S THEOREMS [282] C. THE JORDAN-HÖLDER THEOREM [291] 7. FINITE ABELIAN GROUPS [298] 11. Determinants [304] 1. INTRODUCTION [304] X AXIOMS FOR DETERMINANTS [305] X SOME APPLICATIONS [311] 4. THE CHARACTERISTIC POLYNOMIAL [317] 5. EIGENVALUES AND EIGENVECTORS [324] 0. DETERMINANTS AS VOLUMES [333] 12. Rings of Operators and Differential Equations [341] 1. INTRODUCTION [341] X RINGS AND HOMOMORPHISMS [341] 3. HOMOMORPHISMS OF RINGS [344] 4. THE DIFFERENTIATION OPERATOR [347] 5. SOME DIFFERENTIATION FORMULAS [352] 0. LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [354] 7. FINDING PARTICULAR AND GENERAL SOLUTION [361] «. TRIGONOMETRIC FUNCTIONS [367] 9. SYSTEMS OF EQUATIONS [370] 10. ONE-PARAMETER GROUPS AND INFINITESIMAL GENERATORS [377] 13. The Jordan Normal Form [379] L INTRODUCTION [379] X ELEMENTARY LINEAR MAPPINGS [380] 3. DIRECT SUM DECOMPOSITIONS [382] 4. NILPOTENT MAPPINGS [389] 5. CHARACTERISTIC SUBSPACES [395] 6. THE JORDAN NORMAL FORM [399] 7. UNIQUENESS OF THE JORDAN NORMAL FORM [406] THE PROBLEM OF SIMILARITY [408] ELEMENTARY DIVISORS [411] ELEMENTARY DIVISORS AND SIMILARITY [420] MODULES, TORSION ORDERS, AND THE RATIONAL CANONICAL FORM [423] FINITELY GENERATED ABELIAN GROUPS [431] 14. Quadratic and Hermitian Forms [433] INTRODUCTION [433] LINEAR FUNCTIONS; DUAL SPACES [433] BILINEAR FUNCTIONS [438] QUADRATIC FORMS [441] REDUCTION TO DIAGONAL FORM [446] HERMITIAN FORMS; UNITARY MAPPINGS [452] EUCLIDEAN VECTOR SPACES [459] ORTHONORMAL BASES [462] FOURIER SERIES, BESSEL’S INEQUALITY [467] THE EIGENVALUES OF A HERMITIAN MATRIX [470] SIMULTANEOUS DIAGONALIZATION OF TWO HERMITIAN FORMS [474] UNITARY MATRICES [478] VECTOR PRODUCTS IN ORIENTED 3-SPACE [479] ANALYTIC GEOMETRY IN n DIMENSIONS [486] 15. Quotient Structures [494] MAPPINGS [494] RELATIONS [496] QUOTIENT SET [497] BINARY OPERATIONS ON QUOTIENT SETS [499] THE CONSTRUCTION OF THE FIELD OF QUOTIENTS OF AN INTEGRAL DOMAIN [503] THE CONSTRUCTION OF THE FIELD OF REAL NUMBERS FROM THE FIELD OF RATIONAL NUMBERS [504] THE CONSTRUCTION OF A FIELD CONTAINING A ROOT OF A POLYNOMIAL [508] A PARADOX TO AVOID [510] BERNSTEIN’S THEOREM ON CARDINAL NUMBERS [510]
| Item type | Home library | Shelving location | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A M916 (Browse shelf) | Available | A-2233 |
Contents --
Preface v --
List of Special Symbols xv --
1. Binary Operations and Groups [1] --
1. INTRODUCTION [1] --
2. SETS AND MAPPINGS [1] --
3. BINARY OPERATIONS [5] --
4. THE ASSOCIATIVE AXIOM [8] --
5. THE COMMUTATIVE AXIOM [11] --
6. GROUPS [12] --
7. ISOMORPHISMS AND HOMOMORPHISMS [16] --
8. RESTATEMENT OF THE GROUP AXIOMS [20] --
9. SYSTEMS WITH TWO BINARY OPERATIONS: RINGS, INTEGRAL DOMAINS, --
FIELDS [21] --
2. Rings, Integral Domains, the Integers [28] --
1. INTRODUCTION [28] --
2. SYSTEMS WITH TWO BINARY OPERATIONS: RINGS AND INTEGRAL DOMAINS [28] --
3. ORDERED INTEGRAL DOMAINS [32] --
4. THE SYSTEM OF INTEGERS [36] --
5. SOME COMMENTS [39] --
6. FINITE AND COUNTABLE SETS [42] --
7. MATHEMATICAL INDUCTION AND SOME OF ITS APPLICATIONS [43] --
8. SOME ELEMENTARY NUMBER THEORY [54] --
9. NOTATION FOR INTEGERS [62] --
10. MORE ELEMENTARY NUMBER THEORY: CONGRUENCES [66] --
11. PROOF OF THEOREM 4.4 [77] --
3. Fields, the Rational Numbers [81] --
1. INTRODUCTION [81] --
2. FIELDS [81] --
3. THE FIELD OF RATIONAL NUMBERS [85] --
4. DECIMALS [89] --
5. THE BINOMIAL THEOREM [95] --
4. The Real-number System [100] --
1. INTRODUCTION [100] --
2. CAUCHY SEQUENCES AND LIMITS [102] --
3. THE FIELD OF REAL NUMBERS [100] --
4. SOME PROPERTIES OF R [111] --
5. The Field of Complex Numbers [118] --
1. THE SQUARE ROOT OF -1 [118] --
2. A CONSTRUCTION OF C; QUATERNIONS [122] --
3. A GEOMETRIC INTERPRETATION OF ADDITION AND MULTIPLICATION OF COMPLEX NUMBERS [125] --
4. CAUCHY SEQUENCES AND INFINITE SERIES IN C [129] --
6. Polynomials [133] --
1. INTRODUCTION [133] --
2. INDETERMINATES, OR VARIABLES [133] --
3. FACTORIZATION OF POLYNOMIALS [140] --
4. ROOTS OF POLYNOMIALS [148] --
5. POLYNOMIALS IN SEVERAL VARIABLES [153] --
6. POLYNOMIALS OF DEGREE LESS THAN 5 [158] --
7. Rational Functions [163] --
1. INTRODUCTION [163] --
2. RATIONAL FUNCTIONS [163] --
3. PARTIAL FRACTIONS [165] --
8. Vector Spaces and Affine Spaces [171] --
1. INTRODUCTION [171] --
2. THE BASIC DEFINITIONS [171] --
3. SOME CONSEQUENCES OF THE AXIOMS [172] --
4. SOME IMPORTANT EXAMPLES [174] --
5. SUBSPACES [176] --
9. LINEAR INDEPENDENCE AND DIMENSION [178] --
7. A THEOREM ON LINEAR EQUATIONS [180] --
X ON THE DIMENSION OF VECTOR SPACES [182] --
9. BASE VECTORS [183] --
10. AFFINE SPACES [187] --
11. EUCLIDEAN SPACES [198] --
12. ANALYTIC GEOMETRY [205] --
9. Linear Transformations and Matrices [216] --
1. INTRODUCTION [216] --
2. A NOTATIONAL CONVENTION [216] --
X LINEAR MAPPINGS [217] --
4. OPERATIONS ON LINEAR MAPPINGS [221] --
5. LINEAR TRANSFORMATIONS AND MATRICES [225] --
9. OPERATIONS ON MATRICES [231] --
7. CHANGE OF BASE [238] --
8. RANK OF A MATRIX; LINEAR EQUATIONS; SUBSPACES [242] --
9. REDUCTION TO DIAGONAL FORM [249] --
10. QUOTIENT SPACES [258] --
11 MODULES [261] --
10. Groups and Permutations [266] --
1. INTRODUCTION [266] --
2. BASIC PROPERTIES [266] --
3. PERMUTATIONS [268] --
4. SUBGROUPS AND QUOTIENT GROUPS [275] --
S. TRANSFORMATION GROUPS; SYLOW'S THEOREMS [282] --
C. THE JORDAN-HÖLDER THEOREM [291] --
7. FINITE ABELIAN GROUPS [298] --
11. Determinants [304] --
1. INTRODUCTION [304] --
X AXIOMS FOR DETERMINANTS [305] --
X SOME APPLICATIONS [311] --
4. THE CHARACTERISTIC POLYNOMIAL [317] --
5. EIGENVALUES AND EIGENVECTORS [324] --
0. DETERMINANTS AS VOLUMES [333] --
12. Rings of Operators and Differential Equations [341] --
1. INTRODUCTION [341] --
X RINGS AND HOMOMORPHISMS [341] --
3. HOMOMORPHISMS OF RINGS [344] --
4. THE DIFFERENTIATION OPERATOR [347] --
5. SOME DIFFERENTIATION FORMULAS [352] --
0. LINEAR DIFFERENTIAL EQUATIONS WITH CONSTANT COEFFICIENTS [354] --
7. FINDING PARTICULAR AND GENERAL SOLUTION [361] --
«. TRIGONOMETRIC FUNCTIONS [367] --
9. SYSTEMS OF EQUATIONS [370] --
10. ONE-PARAMETER GROUPS AND INFINITESIMAL GENERATORS [377] --
13. The Jordan Normal Form [379] --
L INTRODUCTION [379] --
X ELEMENTARY LINEAR MAPPINGS [380] --
3. DIRECT SUM DECOMPOSITIONS [382] --
4. NILPOTENT MAPPINGS [389] --
5. CHARACTERISTIC SUBSPACES [395] --
6. THE JORDAN NORMAL FORM [399] --
7. UNIQUENESS OF THE JORDAN NORMAL FORM [406] --
THE PROBLEM OF SIMILARITY [408] --
ELEMENTARY DIVISORS [411] --
ELEMENTARY DIVISORS AND SIMILARITY [420] --
MODULES, TORSION ORDERS, AND THE RATIONAL CANONICAL FORM [423] --
FINITELY GENERATED ABELIAN GROUPS [431] --
14. Quadratic and Hermitian Forms [433] --
INTRODUCTION [433] --
LINEAR FUNCTIONS; DUAL SPACES [433] --
BILINEAR FUNCTIONS [438] --
QUADRATIC FORMS [441] --
REDUCTION TO DIAGONAL FORM [446] --
HERMITIAN FORMS; UNITARY MAPPINGS [452] --
EUCLIDEAN VECTOR SPACES [459] --
ORTHONORMAL BASES [462] --
FOURIER SERIES, BESSEL’S INEQUALITY [467] --
THE EIGENVALUES OF A HERMITIAN MATRIX [470] --
SIMULTANEOUS DIAGONALIZATION OF TWO HERMITIAN FORMS [474] --
UNITARY MATRICES [478] --
VECTOR PRODUCTS IN ORIENTED 3-SPACE [479] --
ANALYTIC GEOMETRY IN n DIMENSIONS [486] --
15. Quotient Structures [494] --
MAPPINGS [494] --
RELATIONS [496] --
QUOTIENT SET [497] --
BINARY OPERATIONS ON QUOTIENT SETS [499] --
THE CONSTRUCTION OF THE FIELD OF QUOTIENTS OF AN INTEGRAL DOMAIN [503] --
THE CONSTRUCTION OF THE FIELD OF REAL NUMBERS FROM THE FIELD OF RATIONAL NUMBERS [504] --
THE CONSTRUCTION OF A FIELD CONTAINING A ROOT OF A POLYNOMIAL [508] --
A PARADOX TO AVOID [510] --
BERNSTEIN’S THEOREM ON CARDINAL NUMBERS [510] --
MR, 27 #4774
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