An R-module M is called an extending module, and also called CS, if it satisfies the following full extending property: For any submodule X of M, there exists a direct summand X * of M, which is an essential extension of X. The concept of this module is a notable property of injective modules, quasi-injective modules, continuous modules, and quasi-continuous modules. In the early days of ring theory, this extending property appeared in Utumi [17] as a von Neumann regular ring R is right continuous if and only if R is an extending module as a right R-module. On the other hand, in [2][3][4], by a quite different method, Harada introduced several extending properties and, simultaneously, lifting properties which are mutually dual notions. These papers not only quickened the progress of the study of continuous and quasi-continuous modules due to Jeremy [8] but also much influenced ring and module theory. For background and applications of extending and lifting properties, the reader is referred to the texts of Harada
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.