Unstable modules over the Steenrod algebra

In this paper we generalize some results of Jmoui and Peterson (J. Pure Appl. Algebra 97 (1994) 37–50) to an odd prime p. In particular, we give a characterization in terms of the action of the Steenrod algebra of those unstable modules which are concentrated in even degrees and admit an injective resolution of which at least the first three terms are reduced.