Notes on pure projective modules

作     者：宋贤梅 陈建龙 Song Xianmei;Chen Jianlong

作者机构：东南大学数学系 

出 版 物：《Journal of Southeast University(English Edition)》 (东南大学学报（英文版）)

年 卷 期：2005年第21卷第4期

页      面：506-508页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：TheTeachingandResearchAwardProgramforOutstandingYoungTeachersinHigherEducationInstitutionsofMOEP.R.C. theResearchFoundationoftheEducationCommitteeofAnhuiProvince(No.2003KJ166) 

主　　题：pure projective left R-module pure injective left R-module pure submodule pure exact sequence 

摘      要：Let R be an associated ring with identity. A new equivalent characterization of pure projective left R-modules is given by applying homological methods. It is proved that a left R-module P is pure projective if and only if for any pure epimorphism E→M→0, where E is pure injective, HomR（P, E）→HomR（P, M）→0 is exact. Also, we obtain a dual result of pure injective left R-modules. Furthermore, it is shown that every pure projective left R-module is closed under pure submodule if and only if every pure injective left R-module is closed under pure epimorphic image.