Iso-Noetherian rings and modules

2019/01/11 by Surya Prakash, G. K. Surya Prakash, Avanish Kumar Chaturvedi +1
Mathematics · Neuroscience · #Rings, Modules, and Algebras #Commutative Algebra and Its Applications #Axon Guidance and Neuronal Signaling

paper · doi:10.1080/00927872.2018.1492591

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.

Citations

• Modules with chain conditions up to isomorphism
• Artinian dimension and isoradical of modules

Related

• Characterization and examples of commutative isoartinian rings
• A new characterization of commutative Artinian rings
• Nil_∗-Noetherian rings
• Almost Noetherian rings and modules
• Non-Noetherianity of Denjoy-Carleman rings of germs