Ideal category of a Noetherian ring

Abstract

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.