A Functor on the Category

Abstract:

      Let _RM_n^l′ be a category which is equivalent to the category of left R-modules.In this paper,we define afunction F:_RM_n^l→_RM_n^l′ and prove that the functor Fpreserves products,direct limits,injections,surjectios and total esactness.Finally,we show that the functor F is a left-adjoint of the inclusion functor I:_RM_n^l′→_RM_n^l. Hence I:_RM_n^l′ is a renective subcategory of _RM_n^l.