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.

Por: Waerden, B. L. van der (Bartel Leendert), 1903-1996Colaborador(es): Artin, Emil, 1898-1962 | Noether, Emmy, 1882-1935 | Benac, Theodore J [trl]Idioma: Inglés Lenguaje original: Alemán Editor: New York : Frederick Ungar, c1950Descripción: ix, 222 p. ; 24 cmOtra clasificación: 00A05
Contenidos:
 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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Libros ordenados por tema 00A05A W127m-2 (Browse shelf) Vol. II Available A-700

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Libros 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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