A Generalization of M-Small Modules

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 that N is M-Rad if and only if; where is the M-injective hull of N. We will show that for a cohereditary module M,R[M] is closed under extension. Let be a module and, the torsion theory cogenerated by is the reject of in, defined as. In this paper we study about the property of this torsion theory. We show that if and only if for every nonzero homomorphism in, . Another attractive result is if and only if, for all. For a module we show that if for some, then the inclusion is M-coRad and also if, then for every submodule of and M-coRad inclusion, we have. Finally for a pseudo projective module M we show that every with is M-Rad and if moreover, then.