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The Tight Integral Closure of a Set of Ideals

✍ Scribed by Melvin Hochster

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
172 KB
Volume
230
Category
Article
ISSN
0021-8693

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✦ Synopsis

This paper celebrates the enormous contributions of David Buchsbaum to commutative algebra, homological algebra, and representation theory, with grateful appreciation for the inspiration he has provided for myself and so many others. Β© 2000 Academic Press * or * . We shall write J for the integral closure of the ideal J, and J * for the tight closure of J. It will turn out that when n = 1, * is simply I 1 . When all of the ideals I t are principal, it will turn out that * is the tight closure of the ideal

Thus, the new notion is a mixture of the notions of tight closure and integral closure. We shall see that * always lies between I 1 + β€’ β€’ β€’ + I n * and I 1 + β€’ β€’ β€’ + I n .

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