Somayeh Karimzadeh, R. Nekooei
Abstract
In this paper, we first obtain equivalent conditions for a module over a Prüfer domain and derive properties of Dedekind modules over such a domain. We then obtain equivalent conditions for a finitely generated Dedekind module over an integrally closed ring. Finally, we characterize multiplication Dedekind modules.
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In this paper, we first obtain equivalent conditions for a module over a Prüfer domain and derive properties of Dedekind modules over such a domain. We then obtain equivalent conditions for a finitely generated Dedekind module over an integrally closed ring. Finally, we characterize multiplication Dedekind modules.
Key concepts: Dedekind cut, Integrally closed, Mathematics, Pure mathematics, Domain (mathematical analysis), Finitely-generated abelian group, Ring (chemistry), Multiplication (music)