Antiisomorphisms of endomorphism rings of modules close to free ones which are induced by morita antiequivalences

The paper deals with antiisomorphisms of endomorphism rings of modules close to free ones (those modules are strong generators, i.e., they contain free cyclic direct summands). A criterion for such antiisomorphisms to be induced by a Morita antiequivalence is obtained. Specifically, any antiisomorphism of endomorphism rings of progenerators (e.g., of matrix rings) is induced by a Morita antiequivalence. Bibliography: 9 titles. © 1997 Plenum Publishing Corporation.