torsion theory cogenerated by a class of modules

we introduce and study a generalization of a class of modules related to radical. the torsion theory cogenerated by this class of modules will be investigated in this paper. we will show that the module n ϵ s[m] is m−radical if and only if for any m− injective module i and any homomorphism f : n →! i in s[m], we have im(f) ⊆ rad(i). also we conclude that n = re_rd[m](n) if and only if for every nonzero homomorphism f : n → k in s[m], im(f) ë rad(k), where rd[m] is the class of all m−radicla modules. the relationship between this modules and some other kind of modules will be studied.