D4-Modules-Reference-Cited by-同舟云学术

D4-Modules

Published:2016-09-09 Issue:09 Volume:16 Page:1750166
ISSN:0219-4988
Container-title:Journal of Algebra and Its Applications
language:en
Short-container-title:J. Algebra Appl.

Author:

Ding Nanqing¹,Ibrahim Yasser²,Yousif Mohamed³,Zhou Yiqiang⁴

Affiliation:

1. Department of Mathematics, Nanjing University, Nanjing, P. R. China

2. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

3. Department of Mathematics, The Ohio State University, Lima, Ohio 45804, USA

4. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John’s, NL, A1C 5S7, Canada

Abstract

A module [Formula: see text] is called a [Formula: see text]-module if, whenever [Formula: see text] and [Formula: see text] are submodules of [Formula: see text] with [Formula: see text] and [Formula: see text] is a homomorphism with [Formula: see text], we have [Formula: see text]. The class of [Formula: see text]-modules contains the [Formula: see text]-modules as well as the dual-square-free (DSF) modules. Furthermore, a [Formula: see text]-module [Formula: see text] is called pseudo-discrete if [Formula: see text] is also a lifting module. In this paper, we study the [Formula: see text]-, 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.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219498817501663

Reference34 articles.

1. D3-Modules

2. ADS modules

3. Classical Artinian Rings and Related Topics

4. Finitistic dimension and a homological generalization of semi-primary rings

5. Some characterizations of uniserial rings

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