On Goldie Extending Modules with Condition (C2)

2016 
A module M is said to be continuous if it is extending with the condition (C2) (cf. [6], [7]). In this article, we consider a 𝒢-extending module with (C2) which is a generalization of a continuous module. First, we show that any 𝒢-extending module with (C2) satisfies the exchange property. We also prove that, if M1 and M2 are 𝒢-extending modules with (C2), then M1 ⊕ M2 is 𝒢-extending with (C2) if and only if Mi is Mj-ejective (i ≠ j).
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