turkmath.org

In this talk, I would like to discuss a generalization of automorphism-invariant module, which is nilpotent-invariant. A module M is called nilpotent-invariant if it is invariant under all nilpotent endomorphisms of its envelope . Some characterizations of nilpotent-invariant modules are studied. We also prove that a nilpotent-invariant module is direct sum of a quasi-injective module and a square-free module. Moreover, some applications of nilpotent-invariant modules are considered and some well-known results are as corollaries. (this work joint with M. Tamer Kosan).