ESSENTIAL EXTENSIONS WITH THE C-EXTENDING PROPERTY
QUAESTIONES MATHEMATICAE, vol.39, no.1, pp.59-64, 2016 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 39 Issue: 1
- Publication Date: 2016
- Doi Number: 10.2989/16073606.2015.1024186
- Journal Name: QUAESTIONES MATHEMATICAE
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.59-64
- Hacettepe University Affiliated: Yes
Abstract
Let C be a nonempty subset of the set of submodules of a module M. Then M is called a C-extending module if for each X in ce there exists a direct summand D of M such that X is essential in D. In general, it is known that an essential extension of a C-extending module is not C-extending. In this paper, our goal is to show how to construct essential extensions of a module which are C extending by using a set of representatives of a certain equivalence relation on the set of all idempotent endomorphisms of the injective hull of the module. Also we characterize when the rational hull of a module is C-extending in terms of such a set of representatives. Moreover we show that several well known types of C-extending conditions (e.g., extending and FI-extending) transfer from module to its rational hull.