Vanishing of derived limits of non-standard inverse systems

It is proved that for certain non-standard versions G ∗ of inverse systems G of R-modules, we have lim n ( G ∗ ) | I = 0 for n > 0 . sult is applied to define a reasonably canonical non-standard resolution for an arbitrary inverse system G of R-modules, such that the application of the inverse limit functor yields a complex whose cohomology groups are isomorphic to the derived limits, lim n . Furthermore, the non-standard resolution gives also the maps lim n g , and the connecting homomorphisms to a reasonable degree. o prove that for miscellaneous types of inverse systems H of modules, the system H is a direct summand of ( H ∗ ) | I .