Özet:

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 the Jacobson radical J(R) of R is nilpotent and Soc(R) is an essential right ideal of R. Moreover, every right Johns ring R is right Kasch, that is, every simple right R-module can be embedded in R. For a M ∈ R-Mod we use the concept of M -annihilator and define a Johns module (resp. quasi-Johns) as a Noetherian module M such that every submodule is an M -annihilator. A module M is called quasi-Johns if any essential submodule of M is an M -annihilator and the set of essential submodules of 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.

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