When Some Complement of an EC-Submodule is a Direct Summand

• Journal title : Kyungpook mathematical journal
• Volume 50, Issue 1,  2010, pp.101-107
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2010.50.1.101
Title & Authors
When Some Complement of an EC-Submodule is a Direct Summand
Denizli, Canan Celep Yucel; Ankara, Adnan Tercan;

Abstract
A module M is said to satisfy the $\small{EC_{11}}$ condition if every ec-submodule of M has a complement which is a direct summand. We show that for a multiplication module over a commutative ring the $\small{EC_{11}}$ and P-extending conditions are equivalent. It is shown that the $\small{EC_{11}}$ property is not inherited by direct summands. Moreover, we prove that if M is an $\small{EC_{11}}$-module where SocM is an ec-submodule, then it is a direct sum of a module with essential socle and a module with zero socle. An example is given to show that the reverse of the last result does not hold.
Keywords
Extending module;ec-closed submodule;P-extending module;$\small{C_{11}}$-module;Multiplication module;
Language
English
Cited by
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