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https://hdl.handle.net/11499/9687
Title: | Essential extensions with the c-extending property | Authors: | Birkenmeier, G.F. Tercan, A. Yücel, Canan Celep |
Keywords: | dense endomorphism ring Extending module FI-extending module fully invariant submodule projection invariant rational hull |
Publisher: | Taylor and Francis Ltd. | Abstract: | Let (Formula presented.) be a nonempty subset of the set of submodules of a module M. Then M is called a (Formula presented.) -extending module if for each X in (Formula presented.) 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 (Formula presented.) -extending module is not (Formula presented.) -extending. In this paper, our goal is to show how to construct essential extensions of a module which are (Formula presented.) 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 (Formula presented.) -extending in terms of such a set of representatives. Moreover we show that several well known types of (Formula presented.) -extending conditions (e.g., extending and FI-extending) transfer from module to its rational hull. © 2016 NISC (Pty) Ltd. | URI: | https://hdl.handle.net/11499/9687 https://doi.org/10.2989/16073606.2015.1024186 |
ISSN: | 1607-3606 |
Appears in Collections: | Fen-Edebiyat Fakültesi Koleksiyonu Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection |
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