Full Ideals |
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| Authors: | Jooyoun Hong Heisook Lee David E Rush |
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| Institution: | 1. Department of Mathematics , Southern Connecticut State University , New Haven , Connecticut , USA;2. Department of Mathematics , Ewha Womans University , Seoul , South Korea;3. Department of Mathematics , University of California , Riverside , California , USA |
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| Abstract: | Contractedness of 𝔪-primary integrally closed ideals played a central role in the development of Zariski's theory of integrally closed ideals in two-dimensional regular local rings (R, 𝔪). In such rings, the contracted 𝔪-primary ideals are known to be characterized by the property that I: 𝔪 = I: x for some x ∈ 𝔪 ?𝔪2. We call the ideals with this property full ideals and compare this class of ideals with the classes of 𝔪-full ideals, basically full ideals, and contracted ideals in higher dimensional regular local rings. The 𝔪-full ideals are easily seen to be full. In this article, we find a sufficient condition for a full ideal to be 𝔪-full. We also show the equivalence of the properties full, 𝔪-full, contracted, integrally closed, and normal, for the class of parameter ideals. We then find a sufficient condition for a basically full parameter ideal to be full. |
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| Keywords: | Basically full ideal Contracted ideal Full ideal m-Full ideal Ideal with Rees property Integrally closed ideal |
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