Please use this identifier to cite or link to this item: http://hdl.handle.net/20.500.11889/8221
Title: Remarks on pseudo-valuation rings
Authors: Badawi, Ayman 
Keywords: Commutative rings;Pseudo-valuation rings
Issue Date: 2000
Abstract: A prime ideal P of a ring A is said to be a strongly prime ideal if aP and bA are comparable for all a,b E A. We shall say that a ring A is a pseudo-valuation ring (PVR) if each prime ideal of A is a strongly prime ideal. We show that if A is a PVR with maximal ideal M, then every overring of A is a PVR if and only if M is a maximal ideal of every overring of A that does not contain the reciprocal of any element of M. We show that if R is an atomic domain and a PVD, then dim(R) < 1. We show that if R is a PVD and a prime ideal of R is finitely generated, then every overring of R is a PVD. We give a characterization of an atomic PVD in terms of the concept of half-factorial domain.
URI: http://hdl.handle.net/20.500.11889/8221
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