Modern algebra. Vol. II / by B. L. van der Waerden ; in part a development from lectures by E. Artin and E. Noether ; translated from the 2d. rev. German ed. by Theodore J. Benac.
Idioma: Inglés Lenguaje original: Alemán Editor: New York : Frederick Ungar, c1950Descripción: ix, 222 p. ; 24 cmOtra clasificación: 00A05CONTENTS CHAPTER XI ELIMINATION THEORY 77. The Resultant System of Several Polynomials in a Single Variable [1] 78. General Elimination Theory [3] 79. Hilbert’s Nullstellensatz [5] 80. Criteria for the Solvability of a System of Homogeneous Equations [6] 81. On Inertia Forms [9] 82. The Resultant of n Forms in n Variables [13] 83. The u-Resultant and the Theorem of Bezout [15] CHAPTER XII GENERAL IDEAL THEORY OF COMMUTATIVE RINGS 84. Basis Condition and Divisor Chain Condition [18] 85. Products and Quotients of Ideals [22] 86. Prime Ideals and Primary Ideals [26] 87. The General Decomposition Theorem [30] 88. The Uniqueness Theorems [34] 89. Theory of Relatively Prime Ideals [38] 90. Single-Primed Ideals [43] CHAPTER XIII THEORY OF POLYNOMIAL IDEALS 91. Algebraic Manifolds [46] 92. Algebraic Functions [49] 93. The Zeros of a Prime Ideal [52] 94. The Dimension [56] 95. The Primary Ideals [58] 96. The Noetherian Theorem [61] 97. Reduction of Multi-dimensional Ideals to Zero-dimensional Ideals [65] 98. Unmixed Ideals [68] CHAPTER XIV INTEGRAL ALGEBRAIC QUANTITIES 99. Finite R-Modules [73] 100. Integral Quantities with Respect to a Ring [75] 101. The Integral Quantities of a Field [78] 102. Axiomatic Foundation of the Classical Theory of Ideals [83] 103. Converse and Extension of the Results [86] 104. Fractional Ideals [90] 105. Ideal Theory of Arbitrary Integrally Closed Domains of Integrity [91] CHAPTER XV LINEAR ALGEBRA 106. Modules. Linear Forms. Vectors. Matrices [97] 107. Modules with Respect to a Skew Field. Linear Equations [103] 108. Modules in Euclidean Rings. Elementary Divisors [106] 109. The Fundamental Theorem of Abelian Groups [110] 110. Representations and Representation Modules [115] 111. Normal Forms of a Matrix in a Commutative Field [119] 112. Elementary Divisors and Characteristic Function [123] 113. Quadratic and Hermitian Forms [125] CHAPTER XVI THEORY OF THE HYPERCOMPLEX QUANTITIES 114. Systems of Hypercomplex Quantities [133] 115. Hypercomplex Systems as Groups with Operators. Generalization [136] 116. Nilpotent Ideals [139] 117. The Complete Reducibility of the Rings without Radical [142] 118. Two-Sided Decomposition and Decomposition of Centrum [147] 119. The Endomorphism Ring of a Completely Reducible Module [151] 120. Structure of the Completely Reducible Rings with Identity [155] 121. The Behavior of the Semi-simple Hypercomplex Systems in the Extension of the Ground Field [158] CHAPTER XVII REPRESENTATION THEORY OF GROUPS AND HYPERCOMPLEX SYSTEMS 122. Statement of the Problem [164] 123. Representation of Hypercomplex Systems [166] 124. The Representations of the Centrum [171] 125. Traces and Characters [173] 126. Representation of Abelian Groups [175] 127. Representations of Finite Groups [179] 128. Group Characters [183] 129. The Representations of the Symmetric Groups [190] 130. Semigroups of Linear Transformations and their Behavior in the Extension of the Ground Field [193] 131. Applications of the Representation Theory to the Theory of the Skew Field [197] 132. The Brauer Classes of Algebras. Characterization of the Splitting Field [203] 133. Cross Products. Factor Sets [207]
Item type | Home library | Shelving location | Call number | Materials specified | Copy number | Status | Date due | Barcode | Course reserves |
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Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A W127m-2 (Browse shelf) | Vol. II | Available | A-700 | |||
Libros | Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 00A05A W127m-2 (Browse shelf) | Vol. II | Ej. 2 | Available | A-2053 |
Traducción de: Moderne Algebra, c1931, 1937, 1940 by Julius Springer, Berlin.
CONTENTS --
CHAPTER XI --
ELIMINATION THEORY --
77. The Resultant System of Several Polynomials in a Single Variable [1] --
78. General Elimination Theory [3] --
79. Hilbert’s Nullstellensatz [5] --
80. Criteria for the Solvability of a System of Homogeneous Equations [6] --
81. On Inertia Forms [9] --
82. The Resultant of n Forms in n Variables [13] --
83. The u-Resultant and the Theorem of Bezout [15] --
CHAPTER XII --
GENERAL IDEAL THEORY OF COMMUTATIVE RINGS --
84. Basis Condition and Divisor Chain Condition [18] --
85. Products and Quotients of Ideals [22] --
86. Prime Ideals and Primary Ideals [26] --
87. The General Decomposition Theorem [30] --
88. The Uniqueness Theorems [34] --
89. Theory of Relatively Prime Ideals [38] --
90. Single-Primed Ideals [43] --
CHAPTER XIII --
THEORY OF POLYNOMIAL IDEALS --
91. Algebraic Manifolds [46] --
92. Algebraic Functions [49] --
93. The Zeros of a Prime Ideal [52] --
94. The Dimension [56] --
95. The Primary Ideals [58] --
96. The Noetherian Theorem [61] --
97. Reduction of Multi-dimensional Ideals to Zero-dimensional Ideals [65] --
98. Unmixed Ideals [68] --
CHAPTER XIV --
INTEGRAL ALGEBRAIC QUANTITIES --
99. Finite R-Modules [73] --
100. Integral Quantities with Respect to a Ring [75] --
101. The Integral Quantities of a Field [78] --
102. Axiomatic Foundation of the Classical Theory of Ideals [83] --
103. Converse and Extension of the Results [86] --
104. Fractional Ideals [90] --
105. Ideal Theory of Arbitrary Integrally Closed Domains of Integrity [91] --
CHAPTER XV --
LINEAR ALGEBRA --
106. Modules. Linear Forms. Vectors. Matrices [97] --
107. Modules with Respect to a Skew Field. Linear Equations [103] --
108. Modules in Euclidean Rings. Elementary Divisors [106] --
109. The Fundamental Theorem of Abelian Groups [110] --
110. Representations and Representation Modules [115] --
111. Normal Forms of a Matrix in a Commutative Field [119] --
112. Elementary Divisors and Characteristic Function [123] --
113. Quadratic and Hermitian Forms [125] --
CHAPTER XVI --
THEORY OF THE HYPERCOMPLEX QUANTITIES --
114. Systems of Hypercomplex Quantities [133] --
115. Hypercomplex Systems as Groups with Operators. Generalization [136] --
116. Nilpotent Ideals [139] --
117. The Complete Reducibility of the Rings without Radical [142] --
118. Two-Sided Decomposition and Decomposition of Centrum [147] --
119. The Endomorphism Ring of a Completely Reducible Module [151] --
120. Structure of the Completely Reducible Rings with Identity [155] --
121. The Behavior of the Semi-simple Hypercomplex Systems in the Extension of the --
Ground Field [158] --
CHAPTER XVII --
REPRESENTATION THEORY OF GROUPS AND HYPERCOMPLEX SYSTEMS --
122. Statement of the Problem [164] --
123. Representation of Hypercomplex Systems [166] --
124. The Representations of the Centrum [171] --
125. Traces and Characters [173] --
126. Representation of Abelian Groups [175] --
127. Representations of Finite Groups [179] --
128. Group Characters [183] --
129. The Representations of the Symmetric Groups [190] --
130. Semigroups of Linear Transformations and their Behavior in the Extension of the --
Ground Field [193] --
131. Applications of the Representation Theory to the Theory of the Skew Field [197] --
132. The Brauer Classes of Algebras. Characterization of the Splitting Field [203] --
133. Cross Products. Factor Sets [207] --
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