Purely and Weakly Purely Cancellation Modules

摘要

The purpose of this paper is to investigate purely cancellation modules. We introduce the concept of purely cancellation module generalizing purely cancellation ideal. We show that an ideal A of R is purely cancellation ideal if and only if AM is purely cancellation module under the condition M is cancellation module various properties and characterizations of purely cancellation module are considered. We also give description for the trace of purely cancellation module.