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024 7 $a10.1515/9781400881796
035   $a(OCoLC)945482788
035   $a(DE-B1597)467965
035   $a(OCoLC)979743245
035   $a(DE-B1597)9781400881796
035   $a(MiAaPQ)EBC4738586
035   $a(EXLCZ)993710000000620150
100   $a20190708d2016      fg              
101 0 $aeng
135   $aurcnu||||||||
181   $ctxt
182   $cc
183   $acr
200 10$aIntroduction to Algebraic K-Theory. (AM-72), Volume 72 /$fJohn Milnor
210  1$aPrinceton, NJ :$cPrinceton University Press,$d[2016]
210  4$d©1972
215   $a1 online resource (200 pages)
225 0 $aAnnals of Mathematics Studies ;$v243
300   $aIncludes index.
311   $a0-691-08101-8 
327   $tFrontmatter --$tPreface and Guide to the Literature --$tContents --$t§1. Projective Modules and K0? --$t§2 . Constructing Projective Modules --$t§3. The Whitehead Group K1? --$t§4. The Exact Sequence Associated with an Ideal --$t§5. Steinberg Groups and the Functor K2 --$t§6. Extending the Exact Sequences --$t§7. The Case of a Commutative Banach Algebra --$t§8. The Product K1? ? K1?  K2? --$t§9. Computations in the Steinberg Group --$t§10. Computation of K2Z --$t§11. Matsumoto's Computation of K2 of a Field --$t12. Proof of Matsumoto's Theorem --$t§13. More about Dedekind Domains --$t§14. The Transfer Homomorphism --$t§15. Power Norm Residue Symbols --$t§16. Number Fields --$tAppendix. Continuous Steinberg Symbols --$tIndex
330   $aAlgebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ? an abelian group K0? or K1? respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.
410  0$aAnnals of mathematics studies ;$vNumber 72.
606   $aAssociative rings
606   $aAbelian groups
606   $aFunctor theory
610   $aAbelian group.
610   $aAbsolute value.
610   $aAddition.
610   $aAlgebraic K-theory.
610   $aAlgebraic equation.
610   $aAlgebraic integer.
610   $aBanach algebra.
610   $aBasis (linear algebra).
610   $aBig O notation.
610   $aCircle group.
610   $aCoefficient.
610   $aCommutative property.
610   $aCommutative ring.
610   $aCommutator.
610   $aComplex number.
610   $aComputation.
610   $aCongruence subgroup.
610   $aCoprime integers.
610   $aCyclic group.
610   $aDedekind domain.
610   $aDirect limit.
610   $aDirect proof.
610   $aDirect sum.
610   $aDiscrete valuation.
610   $aDivision algebra.
610   $aDivision ring.
610   $aElementary matrix.
610   $aElliptic function.
610   $aExact sequence.
610   $aExistential quantification.
610   $aExterior algebra.
610   $aFactorization.
610   $aFinite group.
610   $aFree abelian group.
610   $aFunction (mathematics).
610   $aFundamental group.
610   $aGalois extension.
610   $aGalois group.
610   $aGeneral linear group.
610   $aGroup extension.
610   $aHausdorff space.
610   $aHomological algebra.
610   $aHomomorphism.
610   $aHomotopy.
610   $aIdeal (ring theory).
610   $aIdeal class group.
610   $aIdentity element.
610   $aIdentity matrix.
610   $aIntegral domain.
610   $aInvertible matrix.
610   $aIsomorphism class.
610   $aK-theory.
610   $aKummer theory.
610   $aLattice (group).
610   $aLeft inverse.
610   $aLocal field.
610   $aLocal ring.
610   $aMathematics.
610   $aMatsumoto's theorem.
610   $aMaximal ideal.
610   $aMeromorphic function.
610   $aMonomial.
610   $aNatural number.
610   $aNoetherian.
610   $aNormal subgroup.
610   $aNumber theory.
610   $aOpen set.
610   $aPicard group.
610   $aPolynomial.
610   $aPrime element.
610   $aPrime ideal.
610   $aProjective module.
610   $aQuadratic form.
610   $aQuaternion.
610   $aQuotient ring.
610   $aRational number.
610   $aReal number.
610   $aRight inverse.
610   $aRing of integers.
610   $aRoot of unity.
610   $aSchur multiplier.
610   $aScientific notation.
610   $aSimple algebra.
610   $aSpecial case.
610   $aSpecial linear group.
610   $aSubgroup.
610   $aSummation.
610   $aSurjective function.
610   $aTensor product.
610   $aTheorem.
610   $aTopological K-theory.
610   $aTopological group.
610   $aTopological space.
610   $aTopology.
610   $aTorsion group.
610   $aVariable (mathematics).
610   $aVector space.
610   $aWedderburn's theorem.
610   $aWeierstrass function.
610   $aWhitehead torsion.
615  0$aAssociative rings.
615  0$aAbelian groups.
615  0$aFunctor theory.
676   $a512/.4
700   $aMilnor$b John$040532
801  0$bDE-B1597
801  1$bDE-B1597
906   $aBOOK
912   $a9910154752203321
996   $aIntroduction to Algebraic K-Theory. (AM-72), Volume 72$92780976
997   $aUNINA