The Resource Polytopes, Rings, and K-Theory, by Winfried Bruns, Joseph Gubeladze, (electronic resource)

Polytopes, Rings, and K-Theory, by Winfried Bruns, Joseph Gubeladze, (electronic resource)

Label
Polytopes, Rings, and K-Theory
Title
Polytopes, Rings, and K-Theory
Statement of responsibility
by Winfried Bruns, Joseph Gubeladze
Creator
Contributor
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book treats the interaction between discrete convex geometry, commutative ring theory, algebraic K-theory, and algebraic geometry. The basic mathematical objects are lattice polytopes, rational cones, affine monoids, the algebras derived from them, and toric varieties. The book discusses several properties and invariants of these objects, such as efficient generation, unimodular triangulations and covers, basic theory of monoid rings, isomorphism problems and automorphism groups, homological properties and enumerative combinatorics. The last part is an extensive treatment of the K-theory of monoid rings, with extensions to toric varieties and their intersection theory. This monograph has been written with a view towards graduate students and researchers who want to study the cross-connections of algebra and discrete convex geometry. While the text has been written from an algebraist's view point, also specialists in lattice polytopes and related objects will find an up-to-date discussion of affine monoids and their combinatorial structure. Though the authors do not explicitly formulate algorithms, the book takes a constructive approach wherever possible. Winfried Bruns is Professor of Mathematics at Universität Osnabrück. Joseph Gubeladze is Professor of Mathematics at San Francisco State University
Member of
Is Subseries of
http://library.link/vocab/creatorName
Bruns, Winfried
Dewey number
  • 512.1
  • 512.6
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
  • 0vgn0NT6wtQ
  • SaU2Tz7bBhU
Language note
English
LC call number
QA150-272
Literary form
non fiction
Nature of contents
dictionaries
http://library.link/vocab/relatedWorkOrContributorName
Gubeladze, Joseph.
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Algebra
  • K-theory
  • Discrete groups
  • Algebra
  • Commutative Rings and Algebras
  • K-Theory
  • Convex and Discrete Geometry
Label
Polytopes, Rings, and K-Theory, by Winfried Bruns, Joseph Gubeladze, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 429-443) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties
Dimensions
unknown
Edition
1.
Extent
1 online resource (460 p.)
Form of item
online
Isbn
9781282292147
Media category
computer
Media type code
c
Other control number
10.1007/b105283
Specific material designation
remote
System control number
  • (CKB)1000000000761499
  • (EBL)450646
  • (OCoLC)432702924
  • (SSID)ssj0000773001
  • (PQKBManifestationID)12279230
  • (PQKBTitleCode)TC0000773001
  • (PQKBWorkID)10825551
  • (PQKB)10165271
  • (SSID)ssj0000224364
  • (PQKBManifestationID)11187356
  • (PQKBTitleCode)TC0000224364
  • (PQKBWorkID)10225585
  • (PQKB)10598021
  • (DE-He213)978-0-387-76356-9
  • (MiAaPQ)EBC450646
  • (EXLCZ)991000000000761499
Label
Polytopes, Rings, and K-Theory, by Winfried Bruns, Joseph Gubeladze, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. 429-443) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
I Cones, monoids, and triangulations -- Polytopes, cones, and complexes -- Affine monoids and their Hilbert bases -- Multiples of lattice polytopes -- II Affine monoid algebras -- Monoid algebras -- Isomorphisms and automorphisms -- Homological properties and Hilbert functions -- Gr#x00F6;bner bases, triangulations, and Koszul algebras -- III K-theory -- Projective modules over monoid rings -- Bass#x2013;Whitehead groups of monoid rings -- Varieties
Dimensions
unknown
Edition
1.
Extent
1 online resource (460 p.)
Form of item
online
Isbn
9781282292147
Media category
computer
Media type code
c
Other control number
10.1007/b105283
Specific material designation
remote
System control number
  • (CKB)1000000000761499
  • (EBL)450646
  • (OCoLC)432702924
  • (SSID)ssj0000773001
  • (PQKBManifestationID)12279230
  • (PQKBTitleCode)TC0000773001
  • (PQKBWorkID)10825551
  • (PQKB)10165271
  • (SSID)ssj0000224364
  • (PQKBManifestationID)11187356
  • (PQKBTitleCode)TC0000224364
  • (PQKBWorkID)10225585
  • (PQKB)10598021
  • (DE-He213)978-0-387-76356-9
  • (MiAaPQ)EBC450646
  • (EXLCZ)991000000000761499

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