On the SS-Supplemented Modules Over Dedekind Domains

Abstract

A module M is called ss-supplemented if every submodule U of M has a supplement V in M such that U ∩ V is semisimple. In this paper, we completely determine the structure of (amply) ss-supplemented modules over Dedekind domains. In particular, we prove that an abelian group M is ss-supplemented (as a Z-module) if and only if (Formula presented) where P is the set of all prime integers, I, J are some subsets of P and υ, ν are any index sets. © 2024 Forum-Editrice Universitaria Udinese SRL. All rights reserved.