作者[美]米勒(Miller E.) 著
出版社世界图书出版公司
出版时间2007-10
版次1
装帧平装
上书时间2024-04-05
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图书标准信息
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作者
[美]米勒(Miller E.) 著
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出版社
世界图书出版公司
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出版时间
2007-10
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版次
1
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ISBN
9787506283045
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定价
49.00元
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装帧
平装
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开本
24开
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纸张
胶版纸
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页数
417页
- 【内容简介】
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Thelastdecadehasseenanumberofexcitingdevelopmentsattheintersectionofcommutativealgebrawithcombinatorics.Newmethodshaveevolvedoutofaninfluxofideasfromsuchdiverseareasaspolyhedralgeometry,theoreticalphysics,representationtheory,homologicalalgebra,symplecticgeometry,graphtheory,integerprogramming,symboliccomputation,andstatistics.Thepurposeofthisvolumeistoprovideaselfcontainedintroductiontosomeoftheresultingcombinatorialtechniquesfordealingwithpolynomialrings,semigrouprings,anddeterminantalrings.Ourexpositionmainlyconcernscombinatoriallydefinedidealsandtheirquotients,withafocusonnumericalinvariantsandresolutions,especiallyundergradingsmorerefinedthanthestandardintegergrading.
- 【目录】
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Preface
IMonomialIdeals
1Squarefreemonomialideals
1.1Equivalentdescriptions
1.2Hilbertseries
1.3Simplicialcomplexesandhomology
1.4Monomialmatrices
1.5Bettinumbers
Exercises
Notes
2Borel-fixedmonomialideals
2.1Groupactions
2.2Genericinitialideals
2.3TheEliahou-Kervaireresolution
2.4Lex-segmentideals
Exercises
Notes
3Three-dimensionalstaircases
3.1Monomialidealsintwovariables
3.2Anexamplewithsixmonomials.
3.3TheBuchbergergraph
3.4Genericityanddeformations...
3.5Theplanarresolutionalgorithm.
Exercises
Notes
4Cellularresolutions
4.1Constructionandexactness
4.2BettinumbersandK-polynomials
4.3Examplesofcellularresolutions
4.4Thehullresolution
4.5Subdividingthesimplex
Exercises
Notes
5Alexanderduality
5.1SimplicialAlexanderduality
5.2Generatorsversusirreduciblecomponents.
5.3Dualityforresolutions
5.4Cohullresolutionsandotherapplications
5.5Projectivedimensionandregular!ty
Exercises
Notes
6Genericmonomialideals
6.1Taylorcomplexesandgenericity
6.2TheScarfcomplex
6.3Genericitybydeformation
6.4BoundsonBettinumbers
6.5Cogenericmonomialideals
Exercises
Notes
IIToricAlgebra
7Semigrouprings
7.1Semigroupsandlatticeideals
7.2Affinesemigroupsandpolyhedralcones
7.3Hilbertbases
7.4Initialidealsoflatticeideals
Exercises
Notes
8Multigradedpolynomialrings
8.1Multigradings
8.2HilbertseriesandK-polynomials
8.3MultigradedBettinumbers
8.4K-polynomialsinnonpositivegradings
8.5Multidegrees
Exercises
Notes
9Syzygiesoflatticeideals
9.1Bettinumbers
9.2Laurentmonomialmodules
9.3Freeresolutionsoflatticeideals
9.4GenericityandtheScarfcomplex
Exercises
Notes
……
IIIDeterminants
References
Glossaryofnotation
Index
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