Affiliation:
1. College of Teachers Chengdu University, Chengdu 610106, P. R. China
2. College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, P. R. China
Abstract
It is well known that a domain [Formula: see text] is a Prüfer domain if and only if for [Formula: see text]-modules, relative divisibility implies purity. In this paper, we extend this result to Prüfer [Formula: see text]-multiplication domains (P[Formula: see text]MDs). To do this, we introduce the concept of [Formula: see text]-pure exact sequences over commutative rings with zero divisors, and we prove that a domain [Formula: see text] is a P[Formula: see text]MD if and only if for [Formula: see text]-modules, relative divisibility implies [Formula: see text]-purity. Also, we compare [Formula: see text]-purity with purity and relative divisibility by giving examples.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Algebra and Number Theory
Cited by
7 articles.
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