Artinian ring
If formula_4 is a Noetherian ring and formula_2 is a prime ideal, set formula_6 as the injective hull. The injective hull of formula_7 over the Artinian ring formula_8 can be computed as the module formula_9. It is a module of the same length as formula_8. In particular, for the standard graded ring formula_11 and formula_12, formula_13 is an injective module, giving the tools for computing the indecomposable injective modules for artinian rings over formula_14.