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Adjacent integrally closed ideals in 2-dimensional regular local rings

Title
Adjacent integrally closed ideals in 2-dimensional regular local rings
Authors
Noh S.Watanabe K.-i.
Ewha Authors
노선숙
SCOPUS Author ID
노선숙scopus
Issue Date
2006
Journal Title
Journal of Algebra
ISSN
0021-8693JCR Link
Citation
Journal of Algebra vol. 302, no. 1, pp. 156 - 166
Indexed
SCI; SCIE; SCOPUS WOS scopus
Document Type
Article
Abstract
Let ( A, m ) be a 2-dimensional regular local ring with algebraically closed residue field. Zariski's Unique Factorization Theorem asserts that every integrally closed (complete) m-primary ideal I is uniquely factored into a product of powers of simple complete ideals I = P1 a 1 P2 a 2 ⋯ Pn a n, where Pi is a simple complete ideal for ai {greater than or slanted equal to} 1 and n {greater than or slanted equal to} 1. In this paper, we give a new characterization for a simple complete ideal in terms of adjacent complete ideals. We also give a characterization for a complete ideal I to have finitely many adjacent complete m-primary over-ideals. Namely, we show that I is simple if and only if it has a unique adjacent over-ideal and that I = P1 a 1 P2 a 2 ⋯ Pn a n has only finitely many complete adjacent over-ideals if and only if ai = 1 for every i and there are no proximity relations among Pi. © 2005 Elsevier Inc. All rights reserved.
DOI
10.1016/j.jalgebra.2005.10.034
Appears in Collections:
사범대학 > 수학교육과 > Journal papers
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