Abstract
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.
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