Please use this identifier to cite or link to this item:
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.
Appears in Collections:Fulltext Publications

Files in This Item:
File Description SizeFormat
Remarks on pseudo valuation rings.pdf572.64 kBAdobe PDFView/Open
Show full item record

Page view(s)

checked on Jun 27, 2024


checked on Jun 27, 2024

Google ScholarTM


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.