Algorithmic problem of recognizing automorphisms among endomorphisms of free associative algebras of finite rank

Every Endomorphism of a Local Warfield M

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

✍ Rüdiger Göbel; Ansgar Opdenhövel 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 118 KB

A well-known result of P. Hill's [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.