Explores the classification of absorbing prime multiplication modules in Dedekind domains, suggesting a new perspective.
The main purpose of this article is to present a new approach to the classification of all indecomposable absorbing prime multiplication modules with finite-dimensional top over pullback rings of two Dedekind domains. First, we give a complete description of the absorbing prime multiplication modules over a local Dedekind domain. In fact, we extend the definition and results given in {108} to a more general absorbing prime multiplication modules case. Next, we establish a connection between the absorbing prime multiplication modules and the pure-injective modules over such rings.
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Farzalipour et al. (2024) studied this question.
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