Remarks on pseudo-valuation rings
作者:
Ayman Badawi,
期刊:
Communications in Algebra
(Taylor Available online 2000)
卷期:
Volume 28,
issue 5
页码: 2343-2358
ISSN:0092-7872
年代: 2000
DOI:10.1080/00927870008826964
出版商: Gordon and Breach Science Publishers Ltd.
数据来源: Taylor
摘要:
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 ϵ 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 M 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.
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