Endomorphisms of rank one mixed modules over discrete valuation rings (Q790945)

Let M and N be modules over a discrete valuation ring R, and let \(\Phi:E(M)\to E(N)\) be an isomorphism between their endomorphism algebras. The authors prove that, if M is a mixed R-module of torsion- free rank one whose torsion submodule is simply presented, there exists an isomorphism \(\theta:M\to N\) such that \(\Phi(\alpha)=\theta \alpha \theta^{-1}\) for all \(\alpha \in E(M).\) In particular, all algebra automorphisms of E(M) are inner.