Talk:Injective hull

Not to delete, please. Charles Matthews 19:36, 19 May 2004 (UTC)[reply]

Yes, integral domain (quite late, last night). That sentence: if R is an integral domain, then we take R as R-module for this?

Charles Matthews 09:47, 20 May 2004 (UTC)[reply]

I've added some information, but I'm not convinced that the injective hull of a domain is its field of fractions. References? -CW

Baer's Criterion[edit]

Baer's Criterion should be included with applications: that is, the injective hull of a domain is its field of fractions. Also, mention the structure theorem of injective modules over Noetherian (commutative) rings: that is, indecomposable injectives are the injective hull's of $R/{\mathfrak {p}}$ for ${\mathfrak {p}}$ a prime ideal. Also, mention how to transfer injective modules between rings from a ring morphism: for $\phi :R\to S$ and $I$ injective in $Mod(R)$ we have ${\text{Hom}}_{R}(S,I)$ is an injective $S$ module. — Preceding unsigned comment added by 128.138.65.59 (talk) 23:31, 7 October 2019 (UTC)[reply]

Why should a tool for deciding if a module is injective be mentioned in an article about the injective hull? It's not like its injectivity is in question. Both topics are better placed at injective module, and in fact they are already covered there. Rschwieb (talk) 14:11, 8 October 2019 (UTC)[reply]