Isomorphisms of ring endomorphisms of modules that are close to free (Q922627)

Let A be an associative ring and \(M_ A\) be a right A-module. Then \(M_ A\) is called strong generator if \(M_ A=P\oplus H\), where \(P\cong A_ A\). The author studies the isomorphisms of endomorphism rings of strong generators and proves three criteria answering the question when such isomorphism is induced by the functor \(h^ U=Hom(U\),-) where U is a generator, by Morita equivalence or by some semilinear transformation. As corollaries, the author obtains both some known and some new results.