MODULE CATEGORIES WITH LINEARLY ORDERED CLOSED SUBCATEGORIES

In an earlier paper the first named authors investigated rings whose k ernel functors are linearly ordered. The main tool for describing prop erties of such rings was the filter of ideals associated to a kernel f unctor. In the present paper more generally closed module categories ( i.e. closed under kernels, cokernels and direct sum) with linearly ord ered 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.