Filtered Products of Copies of Injective Modules

We study the transfer of injectivity to filtered products of copies of an injective module. This leads to the introduction of a generalized Noetherian condition, the so-called (ℵ,M)-Noetherian rings. We prove that M is F-injective for every filter F with cpl(F)≥ℵ if and only if R is (ℵ,M)-Noetherian. We also examine the behavior of filtered products of τ-injective torsion-free modules, establishing preservation results under suitable conditions.