  In this paper we describe the categories $\mathbb{L}_R$ , [$\mathbb{R}_R$]
whose objects are left [right] ideals of a Noetherian ring $R$ with unity and
morphisms are appropriate $R$-linear transformations. Further it is shown that
these are preadditive categories with zero object and are full subcategories of
the $R$-modulue category with the property that these are categories with
subobjects and the morphisms admits factorization property.
