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Universitext: A Course in Constructive Algebra
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
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Universitext: A Course in Constructive Algebra - Taschenbuch

1987, ISBN: 9780387966403

[ED: Taschenbuch / Paperback], [PU: Springer, Berlin], AUSFÜHRLICHERE BESCHREIBUNG: The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. INHALT: I. Sets.- 1. Constructive vs. classical mathematics.- 2. Sets, subsets and functions.- 3. Choice.- 4. Categories.- 5. Partially ordered sets and lattices.- 6. Well-founded sets and ordinals.- Notes.- II. Basic Algebra.- 1. Groups.- 2. Rings and fields.- 3. Real numbers.- 4. Modules.- 5. Polynomial rings.- 6. Matrices and vector spaces.- 7. Determinants.- 8. Symmetric polynomials.- Notes.- III. Rings And Modules.- 1. Quasi-regular ideals.- 2. Coherent and Noetherian modules.- 3. Localization.- 4. Tensor products.- 5. Flat modules.- 6. Local rings.- 7. Commutative local rings.- Notes.- IV. Divisibility in Discrete Domains.- 1. Cancellation monoids.- 2. UFD's and Bézout domains.- 3. Dedekind-Hasse rings and Euclidean domains.- 4. Polynomial rings.- Notes.- V. Principal Ideal Domains.- 1. Diagonalizing matrices.- 2. Finitely presented modules.- 3. Torsion modules, p-components, elementary divisors.- 4. Linear transformations.- Notes.- VI. Field Theory.- 1. Integral extensions and impotent rings.- 2. Algebraic independence and transcendence bases.- 3. Splitting fields and algebraic closures.- 4. Separability and diagonalizability.- 5. Primitive elements.- 6. Separability and characteristic p.- 7. Perfect fields.- 8. Galois theory.- Notes.- VII. Factoring Polynomials.- 1. Factorial and separably factorial fields.- 2. Extensions of (separably) factorial fields.- 3. Condition p.- 4. The fundamental theorem of algebra.- Notes.- VIII. Commutative Noetherian Rings.- 1. The Hilbert basis theorem.- 2. Noether normalization and the Artin-Rees lemma.- 3. The Nullstellensatz.- 4. Tennenbaum' s approach to the Hilbert basis theorem.- 5. Primary ideals.- 6. Localization.- 7. Primary decomposition.- 8. Lasker-Noether rings.- 9. Fully Lasker-Noether rings.- 10. The principal ideal theorem.- Notes.- IX. Finite Dimensional Algebras.- 1. Representations.- 2. The density theorem.- 3. The radical and summands.- 4. Wedderburn's theorem, part one.- 5. Matrix rings and division algebras.- Notes.- X. Free Groups.- 1. Existence and uniqueness.- 2. Nielsen sets.- 3. Finitely generated subgroups.- 4. Detachable subgroups of finite-rank free groups.- 5. Conjugate subgroups.- Notes.- XI. Abelian Groups.- 1. Finite-rank torsion-free groups.- 2. Divisible groups.- 3. Height functions on p-groups.- 4. Ulm's theorem.- 5. Construction of Ulm groups.- Notes.- XII. Valuation Theory.- 1. Valuations.- 2. Locally precompact valuations.- 3. Pseudofactorial fields.- 4. Normed vector spaces.- 5. Real and complex fields.- 6. Hensel's lemma.- 7. Extensions of valuations.- 8. e and f.- Notes.- XIII. Dedekind Domains.- 1. Dedekind sets of valuations.- 2. Ideal theory.- 3. Finite extensions., [SC: 0.00], Neuware, gewerbliches Angebot, [GW: 508g]

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A Course in Constructive Algebra - Mines, Ray Richman, Fred Ruitenburg, Wim
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)

Mines, Ray Richman, Fred Ruitenburg, Wim:

A Course in Constructive Algebra - Taschenbuch

ISBN: 9780387966403

[ED: Softcover], [PU: Springer, Berlin], The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. xi, 344 S. 1 SW-Abb., Versandfertig in 3-5 Tagen, [SC: 0.00], Neuware, gewerbliches Angebot

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A Course in Constructive Algebra - Mines, Ray Richman, Fred Ruitenburg, Wim
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Mines, Ray Richman, Fred Ruitenburg, Wim:
A Course in Constructive Algebra - Taschenbuch

ISBN: 9780387966403

[ED: Softcover], [PU: Springer, Berlin], The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr"uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. xi, 344 S. 1 SW-Abb. Sofort lieferbar, [SC: 0.00], Neuware, gewerbliches Angebot

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A Course in Constructive Algebra - Ray Mines
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Ray Mines:
A Course in Constructive Algebra - Taschenbuch

1987, ISBN: 0387966404

ID: 9812709333

[EAN: 9780387966403], Neubuch, [PU: Springer Dez 1987], ALGEBRA, This item is printed on demand - Print on Demand Neuware - The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr'uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit; much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. 344 pp. Englisch

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A Course in Constructive Algebra - Ray Mines
Vergriffenes Buch, derzeit bei uns nicht verfügbar.
(*)
Ray Mines:
A Course in Constructive Algebra - Taschenbuch

ISBN: 9780387966403

[ED: Taschenbuch], [PU: Springer], Neuware - The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr'uctiue analysis in 1967, and by the subtle influences of the proliferation of powerful computers. Bishop demonstrated that pure mathematics can be developed from a constructive point of view while maintaining a continuity with classical terminology and spirit much more of classical mathematics was preserved than had been thought possible, and no classically false theorems resulted, as had been the case in other constructive schools such as intuitionism and Russian constructivism. The computers created a widespread awareness of the intuitive notion of an effecti ve procedure, and of computation in principle, in addi tion to stimulating the study of constructive algebra for actual implementation, and from the point of view of recursive function theory. In analysis, constructive problems arise instantly because we must start with the real numbers, and there is no finite procedure for deciding whether two given real numbers are equal or not (the real numbers are not discrete) . The main thrust of constructive mathematics was in the direction of analysis, although several mathematicians, including Kronecker and van der waerden, made important contributions to construc tive algebra. Heyting, working in intuitionistic algebra, concentrated on issues raised by considering algebraic structures over the real numbers, and so developed a handmaiden'of analysis rather than a theory of discrete algebraic structures. -, [SC: 0.00], Neuware, gewerbliches Angebot, 235x155x19 mm, [GW: 544g]

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A Course in Constructive Algebra
Autor:

Mines, Ray; Richman, Fred; Ruitenburg, Wim

Titel:

A Course in Constructive Algebra

ISBN-Nummer:

9780387966403

The constructive approach to mathematics has recently enjoyed a renaissance. This was caused largely by the appearance of Bishop's Foundations of Constructive Analysis, but also by the proliferation of powerful computers, which stimulated the development of constructive algebra for implementation purposes. In this book, the authors present the fundamental structures of modern algebra from a constructive point of view. Beginning with basic notions, the authors proceed to treat PID's, field theory (including Galois theory), factorisation of polynomials, noetherian rings, valuation theory, and Dedekind domains.

Detailangaben zum Buch - A Course in Constructive Algebra


EAN (ISBN-13): 9780387966403
ISBN (ISBN-10): 0387966404
Taschenbuch
Erscheinungsjahr: 2007
Herausgeber: Springer-Verlag GmbH
360 Seiten
Gewicht: 0,533 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 18.04.2007 11:55:15
Buch zuletzt gefunden am 25.10.2016 08:12:33
ISBN/EAN: 9780387966403

ISBN - alternative Schreibweisen:
0-387-96640-4, 978-0-387-96640-3

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