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ISBN: 9781441986405
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 th… Plus…
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ISBN: 9781441986405
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 th… Plus…
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2012, ISBN: 9781441986405
eBooks, eBook Download (PDF), The constructive approach to mathematics has enjoyed a renaissance, caused in large part by the appearance of Errett Bishop's book Foundations of constr&… Plus…
ISBN: 9781441986405
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 th… Plus…
ISBN: 9781441986405
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 th… Plus…
ISBN: 9781441986405
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 th… Plus…
ISBN: 9781441986405
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 th… Plus…
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Informations détaillées sur le livre - Course in Constructive Algebra
EAN (ISBN-13): 9781441986405
Date de parution: 2012
Editeur: Springer New York
Livre dans la base de données depuis 2016-10-25T08:12:34+02:00 (Paris)
Page de détail modifiée en dernier sur 2024-03-22T17:08:00+01:00 (Paris)
ISBN/EAN: 9781441986405
ISBN - Autres types d'écriture:
978-1-4419-8640-5
Autres types d'écriture et termes associés:
Auteur du livre: mines
Titre du livre: constructive algebra
Données de l'éditeur
Auteur: Ray Mines; Fred Richman; Wim Ruitenburg
Titre: Universitext; A Course in Constructive Algebra
Editeur: Springer; Springer US
344 Pages
Date de parution: 2012-09-10
New York; NY; US
Langue: Anglais
96,29 € (DE)
99,00 € (AT)
118,00 CHF (CH)
Available
XI, 344 p. 1 illus.
EA; E107; eBook; Nonbooks, PBS / Mathematik/Arithmetik, Algebra; Algebra; Verstehen; Galois theory; algebra; field; matrices; matrix; torsion; transformation; B; Algebra; Mathematics and Statistics; BC
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.- 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.- 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.- IV. Divisibility in Discrete Domains.- 1. Cancellation monoids.- 2. UFD's and Bézout domains.- 3. Dedekind-Hasse rings and Euclidean domains.- 4. Polynomial rings.- V. Principal Ideal Domains.- 1. Diagonalizing matrices.- 2. Finitely presented modules.- 3. Torsion modules, p-components, elementary divisors.- 4. Linear transformations.- 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.- VII. Factoring Polynomials.- 1. Factorial and separably factorial fields.- 2. Extensions of (separably) factorial fields.- 3. Condition p.- 4. The fundamental theorem of algebra.- 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.- 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.- 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.- 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.- 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.- XIII. Dedekind Domains.- 1. Dedekind sets of valuations.- 2. Ideal theory.- 3. Finite extensions.Autres livres qui pourraient ressembler au livre recherché:
Dernier livre similaire:
9783540966401 A Course in Constructive Algebra (Mines, Ray, Richman, Fred, Ruitenburg, Wim)
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