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WINTER 2013 Commutative rings whose prime ideals are radically perfect
V. Erdoğdu, S. Harman
J. Commut. Algebra 5(4): 527-544 (WINTER 2013). DOI: 10.1216/JCA-2013-5-4-527

Abstract

The main objective of this paper is to relate the height and the number of generators of ideals in rings that are not necessarily Noetherian. As in [{\bf10, 11}], we call an ideal $I$ of a 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 $I$. This is a generalization of the notion of set theoretic complete intersection of ideals in Noetherian rings to rings that need not be Noetherian. In this work, we determine conditions on a ring $R$ so that the prime ideals of $R$ and also those of the polynomial rings $R[X]$ over $R$ are radically perfect. In many cases, it is shown that the condition of prime ideals of $R$ or that of $R[X]$ being radically perfect is equivalent to a form of the class group of $R$ being torsion.

Citation

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V. Erdoğdu. S. Harman. "Commutative rings whose prime ideals are radically perfect." J. Commut. Algebra 5 (4) 527 - 544, WINTER 2013. https://doi.org/10.1216/JCA-2013-5-4-527

Information

Published: WINTER 2013
First available in Project Euclid: 31 January 2014

zbMATH: 1282.13016
MathSciNet: MR3161745
Digital Object Identifier: 10.1216/JCA-2013-5-4-527

Subjects:
Primary: 13B25 , 13B30 , 13C15 , 13C20 , 13F05 , 13F20
Secondary: 13A15 , 13A18 , 14H50

Keywords: coprime packedness , Hilbert domains , Krull domains , polynomial rings , Prüfer domains , Radically perfectness

Rights: Copyright © 2013 Rocky Mountain Mathematics Consortium

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Vol.5 • No. 4 • WINTER 2013
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