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

Abstract In this paper, we first investigate the relationships between McCoy module and related modules based on their in rings. After that, improve some properties of introduce ZPZC which extend notion modules. We observe structure providing a number examples problems that arise naturally process. Finally, answers to open questions condition are provided.

In this paper we introduce a generalization of M-small modules and discuss about the torsion theory cogenerated by this kind of modules in category . We will use the structure of the radical of a module in  and get some suitable results about this class of modules. Also the relation between injective hull in  and this kind of modules will be investigated in this article.   For a module  we show...

we first characterize $tau$-complemented modules with relative (pre)-covers. we also introduce an extending module relative to $tau$-pure submodules on a hereditary torsion theory $tau$ and give its relationship with $tau$-complemented modules.

We study abstract properties of intervals in the complete lattice of all meet-closed subsets ( -subsemilattices) of a -(meet-)semilattice S, where is an arbitrary cardinal number. Any interval of that kind is an extremally detachable closure system (that is, for each closed set A and each point x outside A, deleting x from the closed set generated by A and x leaves a closed set). Such closure s...