ABSORBING PRIME MULTIPLICATION MODULES OVER A PULLBACK RING

نویسندگان

1 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

doi
10.22044/jas.2022.11638.1593
چکیده

‎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.