Every Endomorphism of a Local Warfield Module of Finite Torsion-Free Rank Is the Sum of Two Automorphisms

A well-known result of P. Hillʹs [1969, Trans. Amer. Math. Soc.141, 99–105] says that any endomorphism of a totally projective abelian p-group for any odd prime is the sum of two automorphisms. We will extend this result to local Warfield modules of finite torsion-free rank over odd primes.