A Note on Injective Modules Over a d.g. Near-Ring

Abstract

In [3] an attempt was made at proving the following result:(A) An N-module M over a d.g. near-ring is injective if and only if for each right ideal u of N and each N-homomorphism f:u→M there exists an element mϵM with f(a) = ma for all aϵu.In this note we present two examples. The first is a counterexample to (A) and the second illustrates one point at which the attempt made in [3] fails.