Module categories with linearly ordered closed subcategories

Abstract

Abstract In an earlier paper the first named authors investigated rings whose kernel functors are linearly ordered. The main tool for describing prop-erties of such rings was the filter of ideals associated to a kernel functor. In the present paper more generally closed module categories (i.e. closed under kernels, cokernels and direct sums) with linearly ordered closed sub-categories are studied. Properties of these categories are given and they are characterized by conditions on special objects, i.e. cogenerators or generators.