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- W2023227035 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 w 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 w and the set of first quadratic transformations of S." @default.
- W2023227035 created "2016-06-24" @default.
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- W2023227035 date "1997-01-01" @default.
- W2023227035 modified "2023-10-14" @default.
- W2023227035 title "Simple complete ideals in two-dimensional regular local rings" @default.
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- W2023227035 doi "https://doi.org/10.1080/00927879708825936" @default.
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