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Integral Closure of Ideals in Excellent Local Rings

✍ Scribed by Donatella Delfino; Irena Swanson

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 258 KB
Volume: 187
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6802

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Let A be a finitely generated module over a (Noetherian) local ring R M . We say that a nonzero submodule B of A is basically full in A if no minimal basis for B can be extended to a minimal basis of any submodule of A properly containing B. We prove that a basically full submodule of A is M-primary

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We show that if R is a commutative ring with identity whose regular ideals are finitely generated, then the integral closure of R is a Krull ring. This is a generalization of the Mori᎐Nagata theorem that the integral closure of a Noethe-Ž .

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✍ B.G. Kang 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 308 KB

Among other things we prove that the integral closure of a Marot ring whose regular ideals are finitely generated is a Krull ring. I: 1993 Academic Press. Inc.

Valuation ideals of order two in 2-dimen

Valuation ideals of order two in 2-dimensional regular local rings

✍ Sunsook Noh 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 233 KB

## Abstract Let __K__ be the quotient field of a 2‐dimensional regular local ring (__R, m__) and let __v__ be a prime divisor of __R__, i.e., a valuation of __K__ birationally dominating __R__ which is residually transcendental over __R__. Zariski showed that: such prime divisor __v__ is uniquely a