An injective-envelope-based characterization of distributive modules over commutative Noetherian rings.

Let R be a commutative Noetherian ring and M be an R-module. The R-module M is called distributive if for every submodules S, T and U of M, the equality S ∩ (T + U) = S ∩ T + S ∩ U holds true. In this paper, we give a necessary and sufficient condition for M to be distributive based on injective envelopes. The proof uses Matlis' results on injective modules. [ABSTRACT FROM AUTHOR]