Commun. Korean Math. Soc. 2023; 38(4): 983-992
Online first article October 18, 2023 Printed October 31, 2023
https://doi.org/10.4134/CKMS.c220332
Copyright © The Korean Mathematical Society.
Rachida EL KHALFAOUI, Najib Mahdou
P. O. Box 1796, University S.M. Ben Abdellah; Box 2202, University S.M. Ben Abdellah
Let $A$ be a ring and $\mathcal{J} = \{\text{ideals $I$ of $A$} \,|\, J(I) = I\}$. The Krull dimension of $A$, written $\dim A$, is the sup of the lengths of chains of prime ideals of $A$; whereas the dimension of the maximal spectrum, denoted by $\dim_\mathcal{J} A$, is the sup of the lengths of chains of prime ideals from $\mathcal{J}$. Then $\dim_{\mathcal{J}} A\leq \dim A$. In this paper, we will study the dimension of the maximal spectrum of some constructions of rings and we will be interested in the transfer of the property $J$-Noetherian to ring extensions.
Keywords: $J$-Noetherian, The dimension of the maximal spectrum of rings, trivial extension, amalgamation of rings
MSC numbers: 13A15, 13E05, 13G05
2010; 25(3): 349-364
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd