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...

PURPOSE Interphotoreceptor retinol-binding protein (IRBP), composed of two or four homologous modules in tandem, plays an important role in retinoid trafficking between the retinal pigmented epithelium, photoreceptors, and Müller cells. The exact nature of this role is not yet clear. Attempts to purify the full-length retinal IRBP to homogeneity for crystallization purposes have largely been un...

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 firstly prove the completeness of the category of crossed modules in a modified category of interest‎. ‎Afterwards‎, ‎we define pullback crossed modules and pullback cat objects that are both obtained by pullback diagrams with extra structures on certain arrows‎. ‎These constructions unify many corresponding results for the cases of groups‎, ‎commutative algebras and can also be adapted to ...