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Keywords:
pullback; separated modules and representations; non-separated modules; comultiplication modules; dedekind domain; pure-injective modules; Prüfer modules
Summary:
First, we give complete description of the comultiplication modules over a Dedekind domain. Second, if $R$ is the pullback of two local Dedekind domains, then we classify all indecomposable comultiplication $R$-modules and establish a connection between the comultiplication modules and the pure-injective modules over such domains.
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