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.
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