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Original Articles

Radically Perfect Prime Ideals in Polynomial Rings Over Prüfer and Pullback Rings

Pages 1377-1385 | Received 23 Jun 2011, Published online: 02 Apr 2013
 

Abstract

In this article, we study the notion of radical perfectness in Prüfer and classical pullbacks issued from valuation domains. We answer positively a question by Erdogdu of whether a domain R such that every prime ideal of the polynomial ring R[X] is radically perfect is one-dimensional. Particularly, we prove that Prüfer and pseudo-valuation domains R over which every prime ideal of the polynomial ring R[X] is radically perfect are one-dimensional domains. Moreover, the class group of such a Prüfer domain is torsion.

2000 Mathematics Subject Classification:

ACKNOWLEDGMENT

I would like to thank to the referee for his/her helpful suggestions which helped in improving the quality of this article.

This work is funded by the Deanship of Scientific Research at KFUPM under Project #SB101026.

Notes

Communicated by I. Swanson.

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