内射包 Injective hull

（重定向自Injective envelope）

在数学中，设 $M$ 为一个含单比特环 $R$ （不一定可交换）上的左模，若左 $R$ -模 $E \supset M$ 是内射模，而且满足下式

N \subset E, N \neq 0 \Rightarrow N \cap M \neq 0 \qquad

（其中

N

是子模）

则称 $E$ 为 $M$ 的一个内射包。类似定义可以照搬至右模的情况。

若模 $M$ 的内射包可以写成不可分解子模的有限直积，则称 $M$ 为有限秩的模。

单词	Injective envelope
释义	Injective envelope 中文百科内射包 Injective hull （重定向自Injective envelope）在数学中，设 $M$ 为一个含单比特环 $R$ （不一定可交换）上的左模，若左 $R$ -模 $E \supset M$ 是内射模，而且满足下式 $N \subset E, N \neq 0 \Rightarrow N \cap M \neq 0 \qquad$ （其中 $N$ 是子模）则称 $E$ 为 $M$ 的一个内射包。类似定义可以照搬至右模的情况。若模 $M$ 的内射包可以写成不可分解子模的有限直积，则称 $M$ 为有限秩的模。英语百科 Injective hull 内射包（重定向自Injective envelope） 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), and are described in detail in the textbook (Lam 1999).
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Injective envelope

内射包 Injective hull

Injective hull 内射包