Abstract:Let M and N be modules over a commutative ring R with N Noetherian. We define the injective capacity of M with respect to N over R to be the supremum of the values t for which N ⊕t embeds into M . In a dual fashion, we deem the number of cogenerators of N with respect to M over R to be the infimum of the numbers t for which N embeds into M ⊕t . We demonstrate that the global injective capacity is the infimum of its local analogues and that the global number of cogenerators is the supremum of the corresponding … Show more
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