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Simple complete ideals in two-dimensional regular local rings

Title
Simple complete ideals in two-dimensional regular local rings
Authors
Noh S.
Ewha Authors
노선숙
SCOPUS Author ID
노선숙scopus
Issue Date
1997
Journal Title
Communications in Algebra
ISSN
0092-7872JCR Link
Citation
Communications in Algebra vol. 25, no. 5, pp. 1563 - 1572
Indexed
SCIE; SCOPUS scopus
Document Type
Article
Abstract
In a two-dimensional regular local ring (R, m), it is known that there exists a unique complete ideal I adjacent to a given simple complete m-primary ideal J from above. In this paper it is shown that there are infinitely many simple complete m-primary ideals adjacent to a given simple complete m-primary ideal J (≠ m) from below whose orders are the same as that of J and that there exists a unique complete m-primary ideal adjacent to J from below whose order is one bigger than that of J. We also show that these are all the complete ideals adjacent to J from below. It is known that there is a unique prime divisor ω and a unique infinitely near point S of R associated to a given simple complete m-primary ideal J. As a corollary of the main theorem, we obtain one-to-one correspondences between the set of simple m-primary complete ideals adjacent to J from below, the set of first neighborhood prime divisors of ω, and the set of first quadratic transformations of S. Copyright © 1997 by Marcel Dekker, Inc.
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사범대학 > 수학교육과 > Journal papers
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