Abstract
A module which is invariant under automorphisms of its injective envelope is called an automorphism-invariant module. The class of automorphism-invariant modules was introduced and investigated by Lee and Zhou in 2013. In this paper, we study the class of modules which are invariant under all nilpotent endomorphisms of their injective envelopes of index two, such as modules are called 2-nilpotent-invariant. Many basic properties are obtained. For instance, it is proved that a nonsingular module [Formula: see text] is a weak duo 2-nilpotent-invariant module if and only if [Formula: see text] is a strongly regular ring. For the ring [Formula: see text] satisfying every cyclic right [Formula: see text]-module is 2-nilpotent-invariant, we prove that [Formula: see text], where [Formula: see text] are rings which satisfy [Formula: see text] is a semi-simple Artinian ring and [Formula: see text] is square-free as a right [Formula: see text]-module and all idempotents of [Formula: see text] is central.
Published Version
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call