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dc.contributor.author노선숙-
dc.date.accessioned2017-01-05T02:01:27Z-
dc.date.available2017-01-05T02:01:27Z-
dc.date.issued2003-
dc.identifier.issn0025-584X-
dc.identifier.otherOAK-1800-
dc.identifier.urihttp://dspace.ewha.ac.kr/handle/2015.oak/233770-
dc.description.abstractLet 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.languageEnglish-
dc.titleValuation ideals of order two in 2-dimensional regular local rings-
dc.typeArticle-
dc.relation.volume261-262-
dc.relation.indexSCIE-
dc.relation.indexSCOPUS-
dc.relation.startpage123-
dc.relation.lastpage140-
dc.relation.journaltitleMathematische Nachrichten-
dc.identifier.doi10.1002/mana.200310116-
dc.identifier.wosidWOS:000187934800008-
dc.identifier.scopusid2-s2.0-0346361634-
dc.author.googleNoh S.-
dc.contributor.scopusid노선숙(8094035900)-
dc.date.modifydate20170104131521-
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사범대학 > 수학교육과 > Journal papers
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