Abstract
In this note we investigate ℵ0-injectivity of rings and modules and review the literature around this topic. We observe that several characterizations of rings by injectivity can be expressed by ℵ0-injectivity. Moreover we point out that the following three classes of rings are not axiomatizable: the right ℵ0-self-injective rings, the right ℵ0-self-injective regular rings and the regular Baer rings.
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