关于F-覆盖的存在性

J4 ›› 2012, Vol. 47 ›› Issue (10): 4-6.

关于F-覆盖的存在性

宋贤梅

安徽师范大学数学系, 安徽芜湖 241000

收稿日期:2011-10-27 出版日期:2012-11-20 发布日期:2012-10-26
作者简介:宋贤梅(1977-), 女, 副教授, 博士, 研究方向为代数学与同调代数. Email:xianmeisong@yahoo.com.cn
基金资助:
国家自然科学基金资助项目(10571026); 安徽省教育厅重点研究项目 (KJ2010A126); 安徽师范大学专项基金(2008xzx10)

Note on the existence of F-covers

SONG Xian-mei

Department of Mathematics, Anhui Normal University, Wuhu 241000, Anhui, China

Received:2011-10-27 Online:2012-11-20 Published:2012-10-26

摘要/Abstract

摘要：

定义了一种模类-广义遗传预挠类F, 即右R-模类F在纯子模,正向极限,纯满像下封闭。证明了若广义遗传预挠类F在扩张下封闭且R∈F,则每一个右R-模有F-覆盖。同时,还得到了当F是广义遗传预挠类时,每一个右R-模有F-预包络当且仅当F在直积下封闭。

关键词: F-覆盖; F-预覆盖; F-预包络

Abstract:

A generalized hereditary pretorsion class F are defined, that is the class of right R-module F is closed under pure submodule, direct limits, and pure homomorphism image. It is shown that if Fis a generalized hereditary pretorsion class closed under extension and R∈F, then every right R-module has an F-cover. And it is proved that if Fis a generalized hereditary pretorsion class, then every right R-module has an F-preenvelope if and only if F is closed under products.

Key words: F-cover; F-precover; F-preenvelope

宋贤梅. 关于F-覆盖的存在性[J]. J4, 2012, 47(10): 4-6.

SONG Xian-mei. Note on the existence of F-covers[J]. J4, 2012, 47(10): 4-6.

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