Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2023; 38(2): 331-340

Online first article December 6, 2022      Printed April 30, 2023

https://doi.org/10.4134/CKMS.c220097

Copyright © The Korean Mathematical Society.

Maximal chain of ideals and $n$-maximal ideal

Hemin A. Ahmad, Parween A. Hummadi

Salahaddin University-Erbil; Salahaddin University-Erbil

Abstract

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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 $K(M.d(K))$.

Keywords: Maximal chain, property $FMC$, Artinian ring, $n$-maximal ideal, maximal dimension, maximal depth, maximal height

MSC numbers: 13E99

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