科研之友
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摘要
Let (R, M) be a two-dimensional Muhly local domain, that is, a two-dimensional integrally closed Noetherian local domain with algebraically closed residue field and with the associated graded ring gr(m)R an integrally closed domain. In this paper we show that a number of fundamental results of Zariski's theory of complete ideals in two-dimensional regular local rings are not necessarily valid in R. However, if the associated graded ring gr(m)R satisfies an additional assumption as in work of Muhly and Sakuma, then we are able to show that "any product of contracted ideals is contracted" holds in R if and only if R has minimal multiplicity.
- 出版日期2013
