Introduction to Algebraic K-Theory. (AM-72), Volume 72 / / John Milnor.

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to a...

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Superior document:Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1972
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 72
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Introduction to Algebraic K-Theory. (AM-72), Volume 72 / John Milnor.
Princeton, NJ : Princeton University Press, [2016]
©1972
1 online resource (200 p.)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
text file PDF rda
Annals of Mathematics Studies ; 72
Frontmatter -- Preface and Guide to the Literature -- Contents -- §1. Projective Modules and K0Λ -- §2 . Constructing Projective Modules -- §3. The Whitehead Group K1Λ -- §4. The Exact Sequence Associated with an Ideal -- §5. Steinberg Groups and the Functor K2 -- §6. Extending the Exact Sequences -- §7. The Case of a Commutative Banach Algebra -- §8. The Product K1Λ ⊗ K1Λ → K2Λ -- §9. Computations in the Steinberg Group -- §10. Computation of K2Z -- §11. Matsumoto's Computation of K2 of a Field -- 12. Proof of Matsumoto's Theorem -- §13. More about Dedekind Domains -- §14. The Transfer Homomorphism -- §15. Power Norm Residue Symbols -- §16. Number Fields -- Appendix. Continuous Steinberg Symbols -- Index
restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star
Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.
Issued also in print.
Mode of access: Internet via World Wide Web.
In English.
Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022)
Abelian groups.
Associative rings.
Functor theory.
MATHEMATICS / Algebra / General. bisacsh
Abelian group.
Absolute value.
Addition.
Algebraic K-theory.
Algebraic equation.
Algebraic integer.
Banach algebra.
Basis (linear algebra).
Big O notation.
Circle group.
Coefficient.
Commutative property.
Commutative ring.
Commutator.
Complex number.
Computation.
Congruence subgroup.
Coprime integers.
Cyclic group.
Dedekind domain.
Direct limit.
Direct proof.
Direct sum.
Discrete valuation.
Division algebra.
Division ring.
Elementary matrix.
Elliptic function.
Exact sequence.
Existential quantification.
Exterior algebra.
Factorization.
Finite group.
Free abelian group.
Function (mathematics).
Fundamental group.
Galois extension.
Galois group.
General linear group.
Group extension.
Hausdorff space.
Homological algebra.
Homomorphism.
Homotopy.
Ideal (ring theory).
Ideal class group.
Identity element.
Identity matrix.
Integral domain.
Invertible matrix.
Isomorphism class.
K-theory.
Kummer theory.
Lattice (group).
Left inverse.
Local field.
Local ring.
Mathematics.
Matsumoto's theorem.
Maximal ideal.
Meromorphic function.
Monomial.
Natural number.
Noetherian.
Normal subgroup.
Number theory.
Open set.
Picard group.
Polynomial.
Prime element.
Prime ideal.
Projective module.
Quadratic form.
Quaternion.
Quotient ring.
Rational number.
Real number.
Right inverse.
Ring of integers.
Root of unity.
Schur multiplier.
Scientific notation.
Simple algebra.
Special case.
Special linear group.
Subgroup.
Summation.
Surjective function.
Tensor product.
Theorem.
Topological K-theory.
Topological group.
Topological space.
Topology.
Torsion group.
Variable (mathematics).
Vector space.
Wedderburn's theorem.
Weierstrass function.
Whitehead torsion.
Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496
print 9780691081014
https://doi.org/10.1515/9781400881796
https://www.degruyter.com/isbn/9781400881796
Cover https://www.degruyter.com/document/cover/isbn/9781400881796/original
language English
format eBook
author Milnor, John,
Milnor, John,
spellingShingle Milnor, John,
Milnor, John,
Introduction to Algebraic K-Theory. (AM-72), Volume 72 /
Annals of Mathematics Studies ;
Frontmatter --
Preface and Guide to the Literature --
Contents --
§1. Projective Modules and K0Λ --
§2 . Constructing Projective Modules --
§3. The Whitehead Group K1Λ --
§4. The Exact Sequence Associated with an Ideal --
§5. Steinberg Groups and the Functor K2 --
§6. Extending the Exact Sequences --
§7. The Case of a Commutative Banach Algebra --
§8. The Product K1Λ ⊗ K1Λ → K2Λ --
§9. Computations in the Steinberg Group --
§10. Computation of K2Z --
§11. Matsumoto's Computation of K2 of a Field --
12. Proof of Matsumoto's Theorem --
§13. More about Dedekind Domains --
§14. The Transfer Homomorphism --
§15. Power Norm Residue Symbols --
§16. Number Fields --
Appendix. Continuous Steinberg Symbols --
Index
author_facet Milnor, John,
Milnor, John,
author_variant j m jm
j m jm
author_role VerfasserIn
VerfasserIn
author_sort Milnor, John,
title Introduction to Algebraic K-Theory. (AM-72), Volume 72 /
title_full Introduction to Algebraic K-Theory. (AM-72), Volume 72 / John Milnor.
title_fullStr Introduction to Algebraic K-Theory. (AM-72), Volume 72 / John Milnor.
title_full_unstemmed Introduction to Algebraic K-Theory. (AM-72), Volume 72 / John Milnor.
title_auth Introduction to Algebraic K-Theory. (AM-72), Volume 72 /
title_alt Frontmatter --
Preface and Guide to the Literature --
Contents --
§1. Projective Modules and K0Λ --
§2 . Constructing Projective Modules --
§3. The Whitehead Group K1Λ --
§4. The Exact Sequence Associated with an Ideal --
§5. Steinberg Groups and the Functor K2 --
§6. Extending the Exact Sequences --
§7. The Case of a Commutative Banach Algebra --
§8. The Product K1Λ ⊗ K1Λ → K2Λ --
§9. Computations in the Steinberg Group --
§10. Computation of K2Z --
§11. Matsumoto's Computation of K2 of a Field --
12. Proof of Matsumoto's Theorem --
§13. More about Dedekind Domains --
§14. The Transfer Homomorphism --
§15. Power Norm Residue Symbols --
§16. Number Fields --
Appendix. Continuous Steinberg Symbols --
Index
title_new Introduction to Algebraic K-Theory. (AM-72), Volume 72 /
title_sort introduction to algebraic k-theory. (am-72), volume 72 /
series Annals of Mathematics Studies ;
series2 Annals of Mathematics Studies ;
publisher Princeton University Press,
publishDate 2016
physical 1 online resource (200 p.)
Issued also in print.
contents Frontmatter --
Preface and Guide to the Literature --
Contents --
§1. Projective Modules and K0Λ --
§2 . Constructing Projective Modules --
§3. The Whitehead Group K1Λ --
§4. The Exact Sequence Associated with an Ideal --
§5. Steinberg Groups and the Functor K2 --
§6. Extending the Exact Sequences --
§7. The Case of a Commutative Banach Algebra --
§8. The Product K1Λ ⊗ K1Λ → K2Λ --
§9. Computations in the Steinberg Group --
§10. Computation of K2Z --
§11. Matsumoto's Computation of K2 of a Field --
12. Proof of Matsumoto's Theorem --
§13. More about Dedekind Domains --
§14. The Transfer Homomorphism --
§15. Power Norm Residue Symbols --
§16. Number Fields --
Appendix. Continuous Steinberg Symbols --
Index
isbn 9781400881796
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9783110442496
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callnumber-first Q - Science
callnumber-subject QA - Mathematics
callnumber-label QA251
callnumber-sort QA 3251.5 M55 41971EB
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https://www.degruyter.com/isbn/9781400881796
https://www.degruyter.com/document/cover/isbn/9781400881796/original
illustrated Not Illustrated
dewey-hundreds 500 - Science
dewey-tens 510 - Mathematics
dewey-ones 512 - Algebra
dewey-full 512/.4
dewey-sort 3512 14
dewey-raw 512/.4
dewey-search 512/.4
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oclc_num 979743245
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hierarchy_parent_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999
is_hierarchy_title Introduction to Algebraic K-Theory. (AM-72), Volume 72 /
container_title Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
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