C4-Modules. Issue 4 (3rd April 2017)

• Record Type: Journal Article
• Authors: Ding, Nanqing; Ibrahim, Yasser; Yousif, Mohamed; Zhou, Yiqiang
• Is Part Of: Communications in algebra. Volume 45:Issue 4(2017)
• Page Start: 1727
• Page End: 1740
• Publication Date: 2017-04-03
• Subjects: C2-modules and C3-modules -- continuous and quasi-continuous modules -- injective and quasi-injective modules -- square-free modules; Primary 16D40, 16D50, 16D60 -- Secondary 16L30, 16L60, 16P20, 16P40, 16P60; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2016.1222412
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: An R -module M is called a C 4-module if, whenever A 1 and A 2 are submodules of M with M = A 1 ⊕ A 2 and f : A 1 → A 2 is an R -homomorphism with ker f ⊆ ⊕ A 1, we have I m f ⊆ ⊕ A 2 . This notion is a non-trivial generalization of both the C 3-modules and the square-free modules. Furthermore, a C 4-module is called pseudo-continuous if it is also a CS -module. In this paper, we give a thorough study of the C 4- and the pseudo-continuous modules.