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.
Acknowledgements
The authors want to thank the referee for the carefully reading and the useful comments to improve this paper. The research of the first named author was partially supported by a grant from UGC.