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Full ideals

Title
Full ideals
Authors
Hong J.Lee H.Noh S.Rush D.E.
Ewha Authors
이혜숙노선숙
SCOPUS Author ID
이혜숙scopusscopus; 노선숙scopus
Issue Date
2009
Journal Title
Communications in Algebra
ISSN
0092-7872JCR Link
Citation
vol. 37, no. 8, pp. 2627 - 2639
Indexed
SCIE; SCOPUS WOS scopus
Abstract
Contractedness of m-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, m). In such rings, the contracted m-primary ideals are known to be characterized by the property that I: m = I: x for some x ∈ m\m2. We call the ideals with this property full ideals and compare this class of ideals with the classes of m-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The m-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be m-full. We also show the equivalence of the properties full, m-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. © Taylor & Francis Group, LLC.
DOI
10.1080/00927870902747340
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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