ESSENTIAL EXTENSIONS WITH THE C-EXTENDING PROPERTY


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

QUAESTIONES MATHEMATICAE, cilt.39, ss.59-64, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 39 Konu: 1
  • Basım Tarihi: 2016
  • Doi Numarası: 10.2989/16073606.2015.1024186
  • Dergi Adı: QUAESTIONES MATHEMATICAE
  • Sayfa Sayıları: ss.59-64

Özet

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.