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A famous result due to L. S. Levy provides a classification of all finitelygenerated indecomposable modules over Dedekind-like rings. This motivates us tooutline an approach to the classification of indecomposable pseudo-absorbingprimary multiplication modules with finite-dimensional top over certain kindsof pullback rings. In this paper, we give a complete classification, up toisomorphism, of all indecomposable pseudo-absorbing primary multiplicationmodules with finite-dimensional top over a pullback of two valuation domainswith the same residue field. We also find a connection between pseudo-absorbingprimary multiplication modules and pure-injective modules over such domains.

On pseudo-absorbing primary multiplication modules over pullback rings