An application of a theorem of Gaschütz

A theorem of Gaschütz is used to prove: Let τ be a homomorphism of the distributively generated near-ring R with identity element and descending chain condition for left modules, τ have finite kernel, and U(R) be the group of units of R; then U(Rτ) = U(R)τ.Furthermore it is shown that the finiteness condition for ker τ can be dropped in the case of R being a ring.