000			05626nam a22003618i 4500
001			CR9781107326002
003			UkCbUP
005			20200124160235.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			130129s2002||||enk o ||1 0|eng|d
020			_a9781107326002 (ebook)
020			_z9780521800785 (hardback)
020			_z9780521106580 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA612.33 _b.M34 2002
082	0	0	_a512/.55 _221
100	1		_aMagurn, Bruce A., _eauthor.
245	1	3	_aAn algebraic introduction to K-theory / _cBruce A. Magurn.
264		1	_aCambridge : _bCambridge University Press, _c2002.
300			_a1 online resource (xiv, 676 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aEncyclopedia of mathematics and its applications ; _vvolume 87
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_gPart I _tGroups of Modules: K[subscript 0] _g15 -- _gChapter 1 _tFree Modules _g17 -- _g1A _tBases _g17 -- _g1B _tMatrix Representations _g26 -- _g1C _tAbsence of Dimension _g38 -- _gChapter 2 _tProjective Modules _g43 -- _g2A _tDirect Summands _g43 -- _g2B _tSummands of Free Modules _g51 -- _gChapter 3 _tGrothendieck Groups _g57 -- _g3A _tSemigroups of Isomorphism Classes _g57 -- _g3B _tSemigroups to Groups _g71 -- _g3C _tGrothendieck Groups _g83 -- _g3D _tResolutions _g95 -- _gChapter 4 _tStability for Projective Modules _g104 -- _g4A _tAdding Copies of R _g104 -- _g4B _tStably Free Modules _g108 -- _g4C _tWhen Stably Free Modules Are Free _g113 -- _g4D _tStable Rank _g120 -- _g4E _tDimensions of a Ring _g128 -- _gChapter 5 _tMultiplying Modules _g133 -- _g5A _tSemirings _g133 -- _g5B _tBurnside Rings _g135 -- _g5C _tTensor Products of Modules _g141 -- _gChapter 6 _tChange of Rings _g160 -- _g6A _tK[subscript 0] of Related Rings _g160 -- _g6B _tG[subscript 0] of Related Rings _g169 -- _g6C _tK[subscript 0] as a Functor _g174 -- _g6D _tThe Jacobson Radical _g178 -- _g6E _tLocalization _g185 -- _gPart II _tSources of K[subscript 0] _g203 -- _gChapter 7 _tNumber Theory _g205 -- _g7A _tAlgebraic Integers _g205 -- _g7B _tDedekind Domains _g212 -- _g7C _tIdeal Class Groups _g224 -- _g7D _tExtensions and Norms _g230 -- _g7E _tK[subscript 0] and G[subscript 0] of Dedekind Domains _g242 -- _gChapter 8 _tGroup Representation Theory _g252 -- _g8A _tLinear Representations _g252 -- _g8B _tRepresenting Finite Groups Over Fields _g265 -- _g8C _tSemisimple Rings _g277 -- _g8D _tCharacters _g300 -- _gPart III _tGroups of Matrices: K[subscript 1] _g317 -- _gChapter 9 _tDefinition of K[subscript 1] _g319 -- _g9A _tElementary Matrices _g319 -- _g9B _tCommutators and K[subscript 1](R) _g322 -- _g9C _tDeterminants _g328 -- _g9D _tThe Bass K[subscript 1] of a Category _g333 -- _gChapter 10 _tStability for K[subscript 1](R) _g342 -- _g10A _tSurjective Stability _g343 -- _g10B _tInjective Stability _g348 -- _gChapter 11 _tRelative K[subscript 1] _g357 -- _g11A _tCongruence Subgroups of GL[subscript n](R) _g357 -- _g11B _tCongruence Subgroups of SL[subscript n](R) _g369 -- _g11C _tMennicke Symbols _g374 -- _gPart IV _tRelations Among Matrices: K[subscript 2] _g399 -- _gChapter 12 _tK[subscript 2](R) and Steinberg Symbols _g401 -- _g12A _tDefinition and Properties of K[subscript 2](R) _g401 -- _g12B _tElements of St(R) and K[subscript 2](R) _g413 -- _gChapter 13 _tExact Sequences _g430 -- _g13A _tThe Relative Sequence _g431 -- _g13B _tExcision and the Mayer-Vietoris Sequence _g456 -- _g13C _tThe Localization Sequence _g481 -- _gChapter 14 _tUniversal Algebras _g488 -- _g14A _tPresentation of Algebras _g489 -- _g14B _tGraded Rings _g493 -- _g14C _tThe Tensor Algebra _g497 -- _g14D _tSymmetric and Exterior Algebras _g505 -- _g14E _tThe Milnor Ring _g518 -- _g14F _tTame Symbols _g534 -- _g14G _tNorms on Milnor K-Theory _g547 -- _g14H _tMatsumoto's Theorem _g557 -- _gPart V _tSources of K[subscript 2] _g567 -- _gChapter 15 _tSymbols in Arithmetic _g569 -- _g15A _tHilbert Symbols _g569 -- _g15B _tMetric Completion of Fields _g572 -- _g15C _tThe p-Adic Numbers and Quadratic Reciprocity _g580 -- _g15D _tLocal Fields and Norm Residue Symbols _g595 -- _gChapter 16 _tBrauer Groups _g610 -- _g16A _tThe Brauer Group of a Field _g610 -- _g16B _tSplitting Fields _g623 -- _g16C _tTwisted Group Rings _g629 -- _g16D _tThe K[subscript 2] Connection _g636 -- _tA Sets, Classes, Functions _g645 -- _gB _tChain Conditions, Composition Series _g647.
520			_aThis is an introduction to algebraic K-theory with no prerequisite beyond a first semester of algebra (including Galois theory and modules over a principal ideal domain). The presentation is almost entirely self-contained, and is divided into short sections with exercises to reinforce the ideas and suggest further lines of inquiry. No experience with analysis, geometry, number theory or topology is assumed. Within the context of linear algebra, K-theory organises and clarifies the relations among ideal class groups, group representations, quadratic forms, dimensions of a ring, determinants, quadratic reciprocity and Brauer groups of fields. By including introductions to standard algebra topics (tensor products, localisation, Jacobson radical, chain conditions, Dedekind domains, semi-simple rings, exterior algebras), the author makes algebraic K-theory accessible to first-year graduate students and other mathematically sophisticated readers. Even if your algebra is rusty, you can read this book; the necessary background is here, with proofs.
650		0	_aK-theory.
776	0	8	_iPrint version: _z9780521800785
830		0	_aEncyclopedia of mathematics and its applications ; _vv. 87.
856	4	0	_uhttps://doi.org/10.1017/CBO9781107326002
999			_c518024 _d518022