ABSTRACT
Before we begin our structural investigation of injective modules, we will determine the closure properties of the class of injective R-modules for various rings R. For an arbitrary ring R the class of injective modules has only two closure properties of significance. One of them we have already seen in Observation 4 of §6.2: the class of injective modules is closed under taking direct summands. The second is given by the following observation.
OBSERVATION 1. The direct product П{Ci | i ∈ Ω} of a family {Ci | i ∈ Ω} of left R-modules is injective if and only if each Ci is injective.
