| 000 | 01352camuu2200325 a 4500 | |
| 001 | 000045406010 | |
| 005 | 20071207135128 | |
| 008 | 040312r20031991nyu b 001 0 eng d | |
| 020 | ▼a 0387406247 (v. 1 : softcover) | |
| 020 | ▼a 0387406255 (v. 2 : softcover) | |
| 035 | ▼a (KERIS)REF000010819637 | |
| 040 | ▼a IWA ▼c IWA ▼d 211009 | |
| 082 | 0 4 | ▼a 512.02 ▼2 22 |
| 090 | ▼a 512.02 ▼b W127m | |
| 100 | 1 | ▼a Waerden, B. L. van der ▼q (Bartel Leendert) , ▼d 1903-. |
| 240 | 1 0 | ▼a Moderne Algebra. ▼l English |
| 245 | 1 0 | ▼a Algebra / ▼c B.L. van der Waerden ; translated by Fred Blum and John R. Schulenberger. |
| 260 | ▼a New York : ▼b Springer-Verlag , ▼c 2003, c1991. | |
| 300 | ▼a 2 v. ; ▼c 24 cm. | |
| 500 | ▼a Translation of: Moderne Algebra. | |
| 500 | ▼a Vol. 2 translated by John R. Schulenberger. | |
| 500 | ▼a "Based in part on lectures by E. Artin and E. Noether." | |
| 500 | ▼a "Originally published in 1970 by Frederick Ungar Publishing Co., Inc., New York"--V. 1, t.p. verso. | |
| 500 | ▼a Translation of Moderne algebra. Vol. 1 is translated from the 7th ed., 1966; vol. 2 from the 5th ed., 1967. | |
| 504 | ▼a Includes bibliographical references and indexes. | |
| 650 | 0 | ▼a Algebra, Abstract. |
| 700 | 1 | ▼a Artin, Emil , ▼d 1898-1962. |
| 700 | 1 | ▼a Noether, Emmy , ▼d 1882-1935. |
| 945 | ▼a KINS |
Holdings Information
| No. | Location | Call Number | Accession No. | Availability | Due Date | Make a Reservation | Service |
|---|---|---|---|---|---|---|---|
| No. 1 | Location Science & Engineering Library/Sci-Info(Stacks2)/ | Call Number 512.02 W127m 1 | Accession No. 121161822 | Availability Available | Due Date | Make a Reservation | Service |
Contents information
Table of Contents
1 Numbers and Sets.- 1.1 Sets.- 1.2 Mappings. Cardinality.- 1.3 The Number Sequence.- 1.4 Finite and Countable (Denumerable) Sets.- 1.5 Partitions.- 2 Groups.- 2.1 The Concept of a Group.- 2.2 Subgroups.- 2.3 Complexes. Cosets.- 2.4 Isomorphisms and Automorphisms.- 2.5 Homomorphisms, Normal Subgroups, and Factor Groups.- 3 Rings and Fields.- 3.1 Rings.- 3.2 Homomorphism and Isomorphism.- 3.3 The Concept of a Field of Quotients.- 3.4 Polynomial Rings.- 3.5 Ideals. Residue Class Rings.- 3.6 Divisibility. Prime Ideals.- 3.7 Euclidean Rings and Principal Ideal Rings.- 3.8 Factorization.- 4 Vector Spaces and Tensor Spaces.- 4.1 Vector Spaces.- 4.2 Dimensional Invariance.- 4.3 The Dual Vector Space.- 4.4 Linear Equations in a Skew Field.- 4.5 Linear Transformations.- 4.6 Tensors.- 4.7 Antisymmetric Multilinear Forms and Determinants.- 4.8 Tensor Products, Contraction, and Trace.- 5 Polynomials.- 5.1 Differentiation.- 5.2 The Zeros of a Polynomial.- 5.3 Interpolation Formulae.- 5.4 Factorization.- 5.5 Irreducibility Criteria.- 5.6 Factorization in a Finite Number of Steps.- 5.7 Symmetric Functions.- 5.8 The Resultant of Two Polynomials.- 5.9 The Resultant as a Symmetric Function of the Roots.- 5.10 Partial Fraction Decomposition.- 6 Theory of Fields.- 6.1 Subfields. Prime Fields.- 6.2 Adjunction.- 6.3 Simple Field Extensions.- 6.4 Finite Field Extensions.- 6.5 Algebraic Field Extensions.- 6.6 Roots of Unity.- 6.7 Galois Fields (Finite Commutative Fields).- 6.8 Separable and Inseparable Extensions.- 6.9 Perfect and Imperfect Fields.- 6.10 Simplicity of Algebraic Extensions. Theorem on the Primitive Element.- 6.11 Norms and Traces.- 7 Continuation of Group Theory.- 7.1 Groups with Operators.- 7.2 Operator Isomorphisms and Operator Homomorphisms.- 7.1 The Two Laws of Isomorphism.- 7.4 Normal Series and Composition Series.- 7.5 Groups of Order pn.- 7.6 Direct Products.- 7.7 Group Characters.- 7.8 Simplicity of the Alternating Group.- 7.9 Transitivity and Primitivity.- 8 The Galois Theory.- 8.1 The Galois Group.- 8.2 The Fundamental Theorem of the Galois Theory.- 8.3 Conjugate Groups, Conjugate Fields, and Elements.- 8.4 Cyclotomic Fields.- 8.5 Cyclic Fields and Pure Equations.- 8.6 Solution of Equations by Radicals.- 8.7 The General Equation of Degree n.- 8.8 Equations of the Second, Third, and Fourth Degrees.- 8.9 Constructions with Ruler and Compass.- 8.10 Calculation of the Galois Group. Equations with a Symmetric Group.- 8.11 Normal Bases.- 9 Ordering and Well Ordering of Sets.- 9.1 Ordered Sets.- 9.2 The Axiom of Choice and Zorn's Lemma.- 9.3 The Well-Ordering Theorem.- 9.4 Transfinite Induction.- 10 Infinite Field Extensions.- 10.1 Algebraically Closed Fields.- 10.2 Simple Transcendental Extensions.- 10.3 Algebraic Dependence and Independence.- 10.4 The Degree of Transcendency.- 10.5 Differentiation of Algebraic Functions.- 11 Real Fields.- 11.1 Ordered Fields.- 11.2 Definition of the Real Numbers.- 11.3 Zeros of Real Functions.- 11.4 The Field of Complex Numbers.- 11.5 Algebraic Theory of Real Fields.- 11.6 Existence Theorems for Formally Real Fields.- 11.7 Sums of Squares.
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