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Maximal chain of ideals and $n$-maximal ideal
Hemin A. Ahmad,Parween A. Hummadi 대한수학회 2023 대한수학회논문집 Vol.38 No.2
In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the $n$-maximal ideal, the maximal dimension of a ring $S$ $(M.\dim(S))$, the maximal depth of an ideal $K$ of $S$ $(M.d(K))$ and maximal height of an ideal $K(M.d(K))$.