The Resource Ideals and reality : projective modules and number of generators of ideals, Friedrich Ischebeck, Ravi A. Rao, (electronic resource)

Ideals and reality : projective modules and number of generators of ideals, Friedrich Ischebeck, Ravi A. Rao, (electronic resource)

Label
Ideals and reality : projective modules and number of generators of ideals
Title
Ideals and reality
Title remainder
projective modules and number of generators of ideals
Statement of responsibility
Friedrich Ischebeck, Ravi A. Rao
Creator
Contributor
Subject
Genre
Language
  • eng
  • eng
Summary
This monograph tells the story of a philosophy of J-P. Serre and his vision of relating that philosophy to problems in affine algebraic geometry. It gives a lucid presentation of the Quillen-Suslin theorem settling Serre's conjecture. The central topic of the book is the question of whether a curve in $n$-space is as a set an intersection of $(n-1)$ hypersurfaces, depicted by the central theorems of Ferrand, Szpiro, Cowsik-Nori, Mohan Kumar, Boratýnski. The book gives a comprehensive introduction to basic commutative algebra, together with the related methods from homological algebra, which will enable students who know only the fundamentals of algebra to enjoy the power of using these tools. At the same time, it also serves as a valuable reference for the research specialist and as potential course material, because the authors present, for the first time in book form, an approach here that is an intermix of classical algebraic K-theory and complete intersection techniques, making connections with the famous results of Forster-Swan and Eisenbud-Evans. A study of projective modules and their connections with topological vector bundles in a form due to Vaserstein is included. Important subsidiary results appear in the copious exercises. Even this advanced material, presented comprehensively, keeps in mind the young student as potential reader besides the specialists of the subject
Member of
Is Subseries of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorName
Ischebeck, Friedrich
Dewey number
512/.42
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA247.3
LC item number
.I78 2005
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
Rao, Ravi A
Series statement
Springer monographs in mathematics,
http://library.link/vocab/subjectName
  • Projective modules (Algebra)
  • Ideals (Algebra)
  • Commutative rings
Label
Ideals and reality : projective modules and number of generators of ideals, Friedrich Ischebeck, Ravi A. Rao, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Basic Commutative Algebra 1; Introduction to Projective Modules; Stably Free Modules; Serre's Conjecture; Continuous Vector Bundles; Basic Commutative Algebra II; Serre's Splitting Theorem and Lindel's Proof of Serre's Conjecture; Regular Rings; Bounds on the Number of Generators; Curves as Complete Intersection
Dimensions
unknown
Extent
1 online resource (346 p.)
Form of item
online
Isbn
9783540263708
Media category
computer
Media type code
  • c
Other control number
10.1007/b137484
Specific material designation
remote
System control number
  • (CKB)1000000000231558
  • (EBL)304059
  • (OCoLC)62776402
  • (SSID)ssj0000176021
  • (PQKBManifestationID)11170387
  • (PQKBTitleCode)TC0000176021
  • (PQKBWorkID)10204361
  • (PQKB)11489475
  • (DE-He213)978-3-540-26370-8
  • (MiAaPQ)EBC304059
  • (EXLCZ)991000000000231558
Label
Ideals and reality : projective modules and number of generators of ideals, Friedrich Ischebeck, Ravi A. Rao, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Content category
text
Content type code
  • txt
Contents
Basic Commutative Algebra 1; Introduction to Projective Modules; Stably Free Modules; Serre's Conjecture; Continuous Vector Bundles; Basic Commutative Algebra II; Serre's Splitting Theorem and Lindel's Proof of Serre's Conjecture; Regular Rings; Bounds on the Number of Generators; Curves as Complete Intersection
Dimensions
unknown
Extent
1 online resource (346 p.)
Form of item
online
Isbn
9783540263708
Media category
computer
Media type code
  • c
Other control number
10.1007/b137484
Specific material designation
remote
System control number
  • (CKB)1000000000231558
  • (EBL)304059
  • (OCoLC)62776402
  • (SSID)ssj0000176021
  • (PQKBManifestationID)11170387
  • (PQKBTitleCode)TC0000176021
  • (PQKBWorkID)10204361
  • (PQKB)11489475
  • (DE-He213)978-3-540-26370-8
  • (MiAaPQ)EBC304059
  • (EXLCZ)991000000000231558

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