Shahrood University of Technology Journal of Algebraic Systems 2345-5128 8 2 2021 01 01 ϕ-ALMOST DEDEKIND RINGS AND $\Phi$-ALMOST DEDEKIND MODULES 141 154 1942 10.22044/jas.2019.8245.1402 EN M. Rahmatinia Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran. A. Yousefian Darani Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran. Journal Article 2019 03 31 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. https://jas.shahroodut.ac.ir/article_1942_b410589f562e99ad20f1a4a2010554ce.pdf