On the integral closure of ideals

被引：28

作者：

Corso A. ^{[1
]}

Huneke C. ^{[1
]}

Vasconcelos W.V. ^{[2
]}

机构：

[1] Department of Mathematics, Purdue University, West Lafayette

[2] Department of Mathematics, Rutgers University, New Brunswick

来源：

manuscripta mathematica | 1998年 / 95卷 / 3期

关键词：

Mathematics Subject Classification (1991): Primary: 13H10; Secondary: 13D40, 13D45, 13H15;

D O I：

10.1007/s002290050033

中图分类号：

学科分类号：

摘要：

Among the several types of closures of an ideal I that have been defined and studied in the past decades, the integral closure Ī has a central place being one of the earliest and most relevant. Despite this role, it is often a difficult challenge to describe it concretely once the generators of I are known. Our aim in this note is to show that in a broad class of ideals their radicals play a fundamental role in testing for integral closedness, and in case I ≠ Ī, √I is still helpful in finding some fresh new elements in Ī\I. Among the classes of ideals under consideration are: complete intersection ideals of codimension two, generic complete intersection ideals, and generically Gorenstein ideals.

引用

页码：331 / 347

页数：16

共 25 条

[1]

Bayer D., Stillman M.E., Macaulay, a Computer Algebra System for Computing in Algebraic Geometry and Commutative Algebra, (1990)

[2]

Bruns W., Herzog J., Cohen-Macaulay Rings, (1993)

[3]

Buchweitz R.-O., Contributions à la Théorie des Singularités, (1981)

[4]

Corso A., Polini C., Links of prime ideals and their rees algebras, J. Algebra, 178, pp. 224-238, (1995)

[5]

Corso A., Polini C., Reduction number of links of irreducible varieties, J. Pure & Applied Algebra, 121, pp. 29-43, (1997)

[6]

Corso A., Polini C., Vasconcelos W.V., Links of prime ideals, Math. Proc. Camb. Phil. Soc., 115, pp. 431-436, (1994)

[7]

Eisenbud D., Commutative Algebra with a View Toward Algebraic Geometry, (1995)

[8]

Eisenbud D., Huneke C., Vasconcelos W.V., Direct methods for primary decomposition, Invent. Math., 110, pp. 207-235, (1992)

[9]

Eisenbud D., Sturmfels B., Binomial ideals, Duke Math. J., 84, pp. 1-45, (1996)

[10]

Goto S., Integral closedness of complete intersection ideals, J. Algebra, 108, pp. 151-160, (1987)

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