Iso-Noetherian rings and modules

Abstract

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

KEYWORDS:

• Epi-Artinian modules
• epi-Noetherian modules
• iso-Artinian modules
• iso-Artinian rings
• iso-Noetherian modules
• iso-Noetherian rings

MATHEMATICS SUBJECT CLASSIFICATION::

• 16P20
• 16P40
• 16P60
• 16P70
• 16E05
• 16E10

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.