Injective hull

This article is about the injective hull of a module in algebra. For injective hulls of metric spaces, also called tight spans, injective envelopes, or hyperconvex hulls, see tight span.

In mathematics, particularly in algebra, the injective hull (or injective envelope) of a module is both the smallest injective module containing it and the largest essential extension of it. Injective hulls were first described in (Eckmann & Schopf 1953).