Valuation ideals of order one in 2-dimensional regular local rings |
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Authors: | Sunsook Noh |
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Institution: | Dept of Math Education , Ewha Womans University , Seoul, 120-75, Korea E-mail: noh@mm.ewha.ac.kr |
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Abstract: | Let υ be a prime divisor of a 2-dimensional regular local ring (R m) with algebraically closed residue field k. Zariski showed that a prime divisor υ of R is uniquely associated to a simple m-primary integrally closed ideal I of R, there exist finitely many simple υ-ideals including I, and all the other υ-ideals can be uniquely factored into products of simple υ-ideals. It is known that such an m-primary ideal I of R can be minimally generated by o(I) + 1 elements.Given a simple integrally closed ideal I of order one with arbitrary rank and its associated prime divisor υ, we find minimal generating sets of all the simple υ-ideals and describe factorizations of all the composite υ-ideals in terms of power products of simple υideals as explicitly as possible. |
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Keywords: | Ordinary character theory Permutation groups |
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