Johns modules and quasi-Johns modules

A right Johns ring is a right Noetherian ring in which every right ideal is a right annihilator. It is known that in a Johns ring R R the Jacobson radical J insert ignore into journalissuearticles values( R ); Jinsert ignore into journalissuearticles values(R); of R R is nilpotent and Soc insert ignore into journalissuearticles values( R ); insert ignore into journalissuearticles values(R); is an essential right ideal of R R . Moreover, every right Johns ring R R is right Kasch, that is, every simple right R R -module can be embedded in R R . For a M ∈ R M∈R -Mod we use the concept of M M -annihilator and define a Johns module  insert ignore into journalissuearticles values(resp. quasi-Johns ); as a Noetherian module M M such that every submodule is an M M -annihilator. A module M M is called quasi-Johns  if any essential submodule of M M is an M M -annihilator and the set of essential submodules of M M satisfies the ascending chain condition. In this paper we extend classical results on Johns rings, as those mentioned above and we also provide new ones. We investigate when a Johns module is Artinian and we give some information about its prime submodules.