ABSTRACT
Chapter 3 A Counter Example for A Question On Pseudo-Valuation Rings Ayman Badawi Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates. abadawi@ausharjah.edu
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.2 Counter Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Abstract In this paper, we give a counter example of the following question which was raised by Anderson, Dobbs, and the author in [3, Question 3.14]: Let G be a strongly prime ideal of a ring D such that G ⊂ Z (D) and (G : G) = T (D) is a PVR. Then T (D) has maximal ideal Z (D)S , where S = D \ Z (D), and Z (D) is a prime ideal of D. Is Z (D) also a strongly prime ideal of D?
