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;
A module M is said to satisfy the 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 and P-extending conditions are equivalent. It is shown that the property is not inherited by direct summands. Moreover, we prove that if M is an -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.