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Weak multiplication modules over a pullback of Dedekind domains

Weak multiplication modules over a pullback of Dedekind domains

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 $M/{\rm Rad} (R) M$ is finite-di