ESSENTIAL EXTENSIONS WITH THE C-EXTENDING PROPERTY

Birkenmeier G. F., TERCAN A., CELEP YÜCEL C.

QUAESTIONES MATHEMATICAE, vol.39, no.1, pp.59-64, 2016 (SCI-Expanded) identifier identifier

  • 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.