Kooperativer Bibliotheksverbund

UID:

Umfang: XIV, 676 S.

Ausgabe: 1.publ.

ISBN: 0-521-80078-1 , 978-0-521-80078-5 , 978-0-521-10658-0

Serie: Encyclopedia of mathematics and its applications 87

Anmerkung: Hier auch später erschienene, unveränderte Nachdrucke

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): K-Theorie ; Einführung ; Lehrbuch

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009818174&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009818174&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA

URL: Inhaltsverzeichnis

URL: Inhaltstext

UID:

Umfang: 1 online resource (xiv, 676 pages) : , digital, PDF file(s).

ISBN: 9781107326002 (ebook)

Serie: Encyclopedia of mathematics and its applications ; volume 87

Inhalt: This 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.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , Groups of Modules: K[subscript 0] , Free Modules , Bases , Matrix Representations , Absence of Dimension , Projective Modules , Direct Summands , Summands of Free Modules , Grothendieck Groups , Semigroups of Isomorphism Classes , Semigroups to Groups , Grothendieck Groups , Resolutions , Stability for Projective Modules , Adding Copies of R , Stably Free Modules , When Stably Free Modules Are Free , Stable Rank , Dimensions of a Ring , Multiplying Modules , Semirings , Burnside Rings , Tensor Products of Modules , Change of Rings , K[subscript 0] of Related Rings , G[subscript 0] of Related Rings , K[subscript 0] as a Functor , The Jacobson Radical , Localization , Sources of K[subscript 0] , Number Theory , Algebraic Integers , Dedekind Domains , Ideal Class Groups , Extensions and Norms , K[subscript 0] and G[subscript 0] of Dedekind Domains , Group Representation Theory , Linear Representations , Representing Finite Groups Over Fields , Semisimple Rings , Characters , Groups of Matrices: K[subscript 1] , Definition of K[subscript 1] , Elementary Matrices , Commutators and K[subscript 1](R) , Determinants , The Bass K[subscript 1] of a Category , Stability for K[subscript 1](R) , Surjective Stability , Injective Stability , Relative K[subscript 1] , Congruence Subgroups of GL[subscript n](R) , Congruence Subgroups of SL[subscript n](R) , Mennicke Symbols , Relations Among Matrices: K[subscript 2] , K[subscript 2](R) and Steinberg Symbols , Definition and Properties of K[subscript 2](R) , Elements of St(R) and K[subscript 2](R) , Exact Sequences , The Relative Sequence , Excision and the Mayer-Vietoris Sequence , The Localization Sequence , Universal Algebras , Presentation of Algebras , Graded Rings , The Tensor Algebra , Symmetric and Exterior Algebras , The Milnor Ring , Tame Symbols , Norms on Milnor K-Theory , Matsumoto's Theorem , Sources of K[subscript 2] , Symbols in Arithmetic , Hilbert Symbols , Metric Completion of Fields , The p-Adic Numbers and Quadratic Reciprocity , Local Fields and Norm Residue Symbols , Brauer Groups , The Brauer Group of a Field , Splitting Fields , Twisted Group Rings , The K[subscript 2] Connection , A Sets, Classes, Functions , Chain Conditions, Composition Series

Weitere Ausg.: Print version: ISBN 9780521800785

Sprache: Englisch

Fachgebiete: Mathematik

Schlagwort(e): Lehrbuch

URL: https://doi.org/10.1017/CBO9781107326002

URL: Volltext

URL: Inhaltstext

UID:

Umfang: XIV, 676 S.

Ausgabe: This digitally print. version (with corr.) 2009

ISBN: 0521106583 , 9780521106580

Serie: Encyclopedia of mathematics and its applications 87

Anmerkung: Originally published: 2002

Sprache: Englisch

URL: Inhaltstext

UID:

Umfang: 1 online resource (xiv, 676 pages) : , digital, PDF file(s).

ISBN: 1-107-08559-4 , 1-139-88293-7 , 1-107-08952-2 , 1-107-09583-2 , 1-107-10391-6 , 1-107-10141-7 , 1-107-32600-1

Serie: Encyclopedia of mathematics and its applications ;

Inhalt: This 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.

Anmerkung: Title from publisher's bibliographic system (viewed on 05 Oct 2015). , pt. I. Groups of modules : Ko -- pt. II. Sources of Ko -- pt. III. Groups of matrices : K1 -- pt. IV. Relations among matrices : K2 -- pt. V. Sources of K2. , English

Weitere Ausg.: ISBN 0-521-10658-3

Weitere Ausg.: ISBN 0-521-80078-1

Sprache: Englisch