Cellular covers of divisible uniserial modules over valuation domains

Abstract

Cellular covers which originate in homotopy theory are considered here for a very special class: divisible uniserial modules over valuation domains. This is a continuation of the study of cellular covers of divisible objects, but in order to obtain more substantial results, we are restricting our attention further to specific covers or to specific kernels. In particular, for h-divisible uniserial modules, we deal first with covers limited to divisible torsion-free modules (Section 3), and continue with the restriction to torsion standard uniserials (Sections 4–5). For divisible non-standard uniserial modules, only those cellular covers are investigated whose kernels are also divisible non-standard uniserials (Section 6). The results are specific enough to enable us to describe more accurately how to find all cellular covers obeying the chosen restrictions.