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Let R be the pullback, in the sense of Levy [J. Algebra 71 (1981)], of two local Dedekind domains. We classify all those indecomposable weak multiplication R-modules M with finite-dimensional top, that is, such that M/Rad(R)M is finitedimensional over R/Rad(R). We also establish a connection between the weak multiplication modules and the pure-injective modules over such domains.

Weak multiplication modules over a pullback of Dedekind domains