组合交换代数

图书标准信息

• 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
• ISBN 9787506283045
• 定价 49.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 417页

【内容简介】

Thelastdecadehasseenanumberofexcitingdevelopmentsattheintersectionofcommutativealgebrawithcombinatorics.Newmethodshaveevolvedoutofaninfluxofideasfromsuchdiverseareasaspolyhedralgeometry，theoreticalphysics，representationtheory，homologicalalgebra，symplecticgeometry，graphtheory，integerprogramming，symboliccomputation，andstatistics.Thepurposeofthisvolumeistoprovideaselfcontainedintroductiontosomeoftheresultingcombinatorialtechniquesfordealingwithpolynomialrings，semigrouprings，anddeterminantalrings.Ourexpositionmainlyconcernscombinatoriallydefinedidealsandtheirquotients，withafocusonnumericalinvariantsandresolutions，especiallyundergradingsmorerefinedthanthestandardintegergrading.

【目录】

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