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

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
VerfasserIn:
Milnor, John,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©1972
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 72
Online Access:
Physical Description:1 online resource (200 p.)
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072 7 |a MAT002000  |2 bisacsh 
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100 1 |a Milnor, John,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Introduction to Algebraic K-Theory. (AM-72), Volume 72 /  |c John Milnor. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©1972 
300 |a 1 online resource (200 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 0 |a Annals of Mathematics Studies ;  |v 72 
505 0 0 |t Frontmatter --   |t Preface and Guide to the Literature --   |t Contents --   |t §1. Projective Modules and K0Λ --   |t §2 . Constructing Projective Modules --   |t §3. The Whitehead Group K1Λ --   |t §4. The Exact Sequence Associated with an Ideal --   |t §5. Steinberg Groups and the Functor K2 --   |t §6. Extending the Exact Sequences --   |t §7. The Case of a Commutative Banach Algebra --   |t §8. The Product K1Λ ⊗ K1Λ → K2Λ --   |t §9. Computations in the Steinberg Group --   |t §10. Computation of K2Z --   |t §11. Matsumoto's Computation of K2 of a Field --   |t 12. Proof of Matsumoto's Theorem --   |t §13. More about Dedekind Domains --   |t §14. The Transfer Homomorphism --   |t §15. Power Norm Residue Symbols --   |t §16. Number Fields --   |t Appendix. Continuous Steinberg Symbols --   |t Index 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
520 |a 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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Abelian groups. 
650 0 |a Associative rings. 
650 0 |a Functor theory. 
650 7 |a MATHEMATICS / Algebra / General.  |2 bisacsh 
653 |a Abelian group. 
653 |a Absolute value. 
653 |a Addition. 
653 |a Algebraic K-theory. 
653 |a Algebraic equation. 
653 |a Algebraic integer. 
653 |a Banach algebra. 
653 |a Basis (linear algebra). 
653 |a Big O notation. 
653 |a Circle group. 
653 |a Coefficient. 
653 |a Commutative property. 
653 |a Commutative ring. 
653 |a Commutator. 
653 |a Complex number. 
653 |a Computation. 
653 |a Congruence subgroup. 
653 |a Coprime integers. 
653 |a Cyclic group. 
653 |a Dedekind domain. 
653 |a Direct limit. 
653 |a Direct proof. 
653 |a Direct sum. 
653 |a Discrete valuation. 
653 |a Division algebra. 
653 |a Division ring. 
653 |a Elementary matrix. 
653 |a Elliptic function. 
653 |a Exact sequence. 
653 |a Existential quantification. 
653 |a Exterior algebra. 
653 |a Factorization. 
653 |a Finite group. 
653 |a Free abelian group. 
653 |a Function (mathematics). 
653 |a Fundamental group. 
653 |a Galois extension. 
653 |a Galois group. 
653 |a General linear group. 
653 |a Group extension. 
653 |a Hausdorff space. 
653 |a Homological algebra. 
653 |a Homomorphism. 
653 |a Homotopy. 
653 |a Ideal (ring theory). 
653 |a Ideal class group. 
653 |a Identity element. 
653 |a Identity matrix. 
653 |a Integral domain. 
653 |a Invertible matrix. 
653 |a Isomorphism class. 
653 |a K-theory. 
653 |a Kummer theory. 
653 |a Lattice (group). 
653 |a Left inverse. 
653 |a Local field. 
653 |a Local ring. 
653 |a Mathematics. 
653 |a Matsumoto's theorem. 
653 |a Maximal ideal. 
653 |a Meromorphic function. 
653 |a Monomial. 
653 |a Natural number. 
653 |a Noetherian. 
653 |a Normal subgroup. 
653 |a Number theory. 
653 |a Open set. 
653 |a Picard group. 
653 |a Polynomial. 
653 |a Prime element. 
653 |a Prime ideal. 
653 |a Projective module. 
653 |a Quadratic form. 
653 |a Quaternion. 
653 |a Quotient ring. 
653 |a Rational number. 
653 |a Real number. 
653 |a Right inverse. 
653 |a Ring of integers. 
653 |a Root of unity. 
653 |a Schur multiplier. 
653 |a Scientific notation. 
653 |a Simple algebra. 
653 |a Special case. 
653 |a Special linear group. 
653 |a Subgroup. 
653 |a Summation. 
653 |a Surjective function. 
653 |a Tensor product. 
653 |a Theorem. 
653 |a Topological K-theory. 
653 |a Topological group. 
653 |a Topological space. 
653 |a Topology. 
653 |a Torsion group. 
653 |a Variable (mathematics). 
653 |a Vector space. 
653 |a Wedderburn's theorem. 
653 |a Weierstrass function. 
653 |a Whitehead torsion. 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press eBook-Package Archive 1927-1999  |z 9783110442496 
776 0 |c print  |z 9780691081014 
856 4 0 |u https://doi.org/10.1515/9781400881796 
856 4 0 |u https://www.degruyter.com/isbn/9781400881796 
856 4 2 |3 Cover  |u https://www.degruyter.com/document/cover/isbn/9781400881796/original 
912 |a 978-3-11-044249-6 Princeton University Press eBook-Package Archive 1927-1999  |c 1927  |d 1999 
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