D4-Modules

被引：28

作者：

Ding, Nanqing ^{[1
]}

Ibrahim, Yasser ^{[2
]}

Yousif, Mohamed ^{[3
]}

Zhou, Yiqiang ^{[4
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing, Jiangsu, Peoples R China

[2] Cairo Univ, Fac Sci, Dept Math, Giza, Egypt

[3] Ohio State Univ, Dept Math, Lima, OH 45804 USA

[4] Mem Univ Newfoundland, Dept Math & Stat, St John, NF A1C 5S7, Canada

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2017年 / 16卷 / 09期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Clean module; D3-module; D4-module; D4-cover; dual-square-free module; exchange property; lifting module; quasi-projective module; direct-projective module; pseudo-projective module; quasi-discrete module; pseudo-discrete module; UNISERIAL RINGS; EXCHANGE PROPERTY; DISCRETE MODULES; REPRESENTATIONS;

D O I：

10.1142/S0219498817501663

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A module M is called a D4-module if, whenever A and B are submodules of M with M = A circle plus B and f : A -> B is a homomorphism with Imf subset of(circle plus) B, we have kerf subset of(circle plus) A. The class of D4-modules contains the D3-modules as well as the dual-square-free (DSF) modules. Furthermore, a D4-module M is called pseudo-discrete if M is also a lifting module. In this paper, we study the D4-, the DSF, and the pseudo-discrete modules, and show that a pseudo-discrete module is clean iff it has the finite exchange property iff it has the full exchange property.

引用

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