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Algebra

Author: B L van der Waerden; Emil Artin; Emmy Noether
Publisher: New York : Springer-Verlag, ©1991.
Edition/Format:   Print book : EnglishView all editions and formats
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Based in part on lectures by E. Artin and E. Noether

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Additional Physical Format: Online version:
Waerden, B.L. van der (Bartel Leendert), 1903-
Algebra.
New York : Springer-Verlag, ©1991
(OCoLC)679571605
Document Type: Book
All Authors / Contributors: B L van der Waerden; Emil Artin; Emmy Noether
ISBN: 0387974245 9780387974248 3540974245 9783540974246 0387974253 9780387974255 3540974253 9783540974253
OCLC Number: 23098679
Notes: Translation of: Moderne Algebra.
Vol. 2 translated by John R. Schulenberger.
"Based in part on lectures by E. Artin and E. Noether."
"Originally published in 1970 by Frederick Ungar Publishing Co., Inc., New York"--V. 1, t.p. verso.
Description: 2 volumes ; 24 cm
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.
Other Titles: Moderne Algebra.
Responsibility: B.L. van der Waerden ; translated by Fred Blum and John R. Schulenberger.

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From the reviews: "The book ... is a reprinted version of the original English translation of the first volume of B. L. van der Waerden's 'Algebra', without any alterations. However, it is the first Read more...

 
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