Document Type: Original Manuscript


Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran.



The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and obtain the relationship between $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules.