Full metadata record
DC Field | Value | Language |
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dc.contributor.author | 노선숙 | - |
dc.date.accessioned | 2017-01-05T02:01:27Z | - |
dc.date.available | 2017-01-05T02:01:27Z | - |
dc.date.issued | 2003 | - |
dc.identifier.issn | 0025-584X | - |
dc.identifier.other | OAK-1800 | - |
dc.identifier.uri | https://dspace.ewha.ac.kr/handle/2015.oak/233770 | - |
dc.description.abstract | Let K be the quotient field of a 2-dimensional regular local ring (R, m) and let v be a prime divisor of R, i.e., a valuation of K birationally dominating R which is residually transcendental over R. Zariski showed that: such prime divisor v is uniquely associated to a simple m-primary integrally closed ideal I of R, there are only finitely many simple v-ideals including I, and all the other v-ideals can be uniquely factored into products of simple v-ideals. The number of nonmaximal simple v-ideals is called the rank of v or the rank of I as well. It is also known that such an m-primary ideal I is minimally generated by o(I) +1 elements, where o(I) denotes the m-adic order of I. Given a simple valuation ideal of order two associated to a prime divisor v of arbitrary rank, in this paper we find minimal generating sets of all the simple v-ideals and the value semigroup v(R) in terms of its rank and the v-value difference of two elements in a regular system of parameters of R. We also obtain unique factorizations of all the composite v-ideals and describe the complete sequence of v-ideals as explicitly as possible. © 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. | - |
dc.language | English | - |
dc.title | Valuation ideals of order two in 2-dimensional regular local rings | - |
dc.type | Article | - |
dc.relation.volume | 261-262 | - |
dc.relation.index | SCIE | - |
dc.relation.index | SCOPUS | - |
dc.relation.startpage | 123 | - |
dc.relation.lastpage | 140 | - |
dc.relation.journaltitle | Mathematische Nachrichten | - |
dc.identifier.doi | 10.1002/mana.200310116 | - |
dc.identifier.wosid | WOS:000187934800008 | - |
dc.identifier.scopusid | 2-s2.0-0346361634 | - |
dc.author.google | Noh S. | - |
dc.contributor.scopusid | 노선숙(8094035900) | - |
dc.date.modifydate | 20170104131521 | - |