- Hacettepe Journal of Mathematics and Statistics
- Vol: 51 Issue: 4
- Johns modules and quasi-Johns modules
Johns modules and quasi-Johns modules
Authors : Jaime Castro Pérez, Mauricio Gabriel Medina-bárcenas
Pages : 1029-1046
Doi:10.15672/hujms.902650
View : 12 | Download : 6
Publication Date : 2022-08-01
Article Type : Research
Abstract :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 ( R ) J(R) of R R is nilpotent and Soc ( R ) (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 (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.Keywords : Johns module, Noetherian module, M-annihlator, Kasch module, (semi)prime submodule, projective module