Exchange PF-rings and almost PP-rings
type: Item
instance of: scholarly article
title: Exchange PF-rings and almost PP-rings
zbMATH Open document ID: 0692.13007
DOI: 10.1155/S016117128900089X
author: H. Al-Ezeh
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46444
review text: Recall that a commutative ring R with unity is called PF-ring (respectively PP-ring) if every principal ideal is a flat (respectively projective) R-module. A relation between PF-rings and almost PP-rings is established by proving the following theorems. Theorem 1. Any exchange PF-ring is an almost PP-PM-ring. Theorem 2. Any almost PP-PM-ring is an exchange PF-ring. Theorem 3. Let X be a completely regular Hausdorff space. Then the ring C(X) of all continuous real-valued functions on X is an almost PP-ring if and only if it is a U-ring. Some examples are also given. For instance, the ring of the integers is an almost PP-ring, which is not a PM-ring and so not an exchange ring.
Mathematics Subject Classification ID: 13C13
Mathematics Subject Classification ID: 54C40
zbMATH DE Number: 4132304
zbMATH Keywords: ring of continuous real-valued functions
zbMATH Keywords: exchange PF-ring
zbMATH Keywords: almost PP- ring
MaRDI profile type: Publication
Recommended article: Q4016760
Recommended article: On P-exchange rings
Recommended article: Q4214881
Recommended article: Exchange rings, related comparability and power-substitution
Recommended article: Q5148159
Recommended article: Extensions of exchange rings
Recommended article: Exchange rings and their extensions
Recommended article: Rings and modules with exchange properties
Recommended article: Exchange rings satisfying the related comparability
Recommended article: On PP-rings
description: scientific article; zbMATH DE number 4132304