Shahrood University of Technology Journal of Algebraic Systems 2345-5128 11 2 2024 01 01 ABSORBING PRIME MULTIPLICATION MODULES OVER A PULLBACK RING 33 51 2729 10.22044/jas.2022.11638.1593 EN Farkhondeh Farzalipour Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. Peyman Ghiasvand Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. Journal Article 2022 02 06 ‎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 \cite{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. https://jas.shahroodut.ac.ir/article_2729_023ba765031d3b4ae873cbaa59711efd.pdf