Abstract
The Hilbert basis theorem says that if a ring R is Noetherian, then the polynomial ring is Noetherian. But, in the case of an Artinian ring R, the polynomial ring is not Artinian. In this paper, our main aim is to show that if R is iso-Noetherian (iso-Artinian), then the polynomial ring is iso-Noetherian (iso-Artinian). Also, we investigate some properties of iso-Noetherian (iso-Artinian) rings and modules.
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