Radically perfect prime ideals in polynomial rings |
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Authors: | Vahap Erdoğdu |
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Institution: | 1. Department of Mathematics, Istanbul Technical University, Maslak, 80626, Istanbul, Turkey
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Abstract: | We call an ideal I of a commutative ring R radically perfect if among the ideals of R whose radical is equal to the radical of I the one with the least number of generators has this number of generators equal to the height of I. Let R be a Noetherian integral domain of Krull dimension one containing a field of characteristic zero. Then each prime ideal of
the polynomial ring RX] is radically perfect if and only if R is a Dedekind domain with torsion ideal class group. We also show that over a finite dimensional Bézout domain R, the polynomial ring RX] has the property that each prime ideal of it is radically perfect if and only if R is of dimension one and each prime ideal of R is the radical of a principal ideal. |
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