Modules in which kernels of endomorphisms are invariant under all automorphisms

A right [Formula: see text]-module [Formula: see text] is called kernel-invariant (under automorphisms) if the kernels of all endomorphisms of [Formula: see text] are invariant under all automorphisms of [Formula: see text]. We show that the classes of kernel-invariant modules and rings inherit some of the important features of the aforementioned classes of modules and rings. For example, [Formula: see text] Duo modules and uniform non-singular modules are kernel-invariant, [Formula: see text] Endomorphism rings of kernel-invariant modules are kernel-invariant and they are abelian, [Formula: see text] Domains are kernel-invariant which are not auto-invariant, [Formula: see text] Semicommutative rings are kernel-invariant and the converse is true if they are clean.