Krull Dimension in Power Series Ring Over an Almost Pseudo-Valuation Domain |
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Authors: | Mohamed Khalifa Ali Benhissi |
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Institution: | 1. Department of Mathematics, Faculty of Sciences , Monastir, Tunisia kmhoalg@yahoo.fr;3. Department of Mathematics, Faculty of Sciences , Monastir, Tunisia |
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Abstract: | Let R be an integral domain. We say that R is a star-domain if R has at least a height one prime ideal and if for each height one prime ideal P of R, R satisfies the acc on P-principal ideals (i.e., ideals of the form aP, a ∈ R). We prove that if R is an APVD with nonzero finite Krull dimension, then the power series ring RX]] has finite Krull dimension if and only if R is a residually star-domain (i.e., for each nonmaximal prime ideal P of R, R/P is a star-domain) if and only if RX]] is catenarian. |
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Keywords: | APVD Krull dimension Power series ring |
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