• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.101-107
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• 2010

A module M is said to satisfy the $EC_{11}$ 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 $EC_{11}$ and P-extending conditions are equivalent. It is shown that the $EC_{11}$ property is not inherited by direct summands. Moreover, we prove that if M is an $EC_{11}$-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.