Dergiler / International Electronic Journal of Algebra / 2023 / Cilt: 34 Sayı: 34

Nil$_{\ast}$-Artinian rings

Nil$_{\ast}$-Artinian rings

Xiaolei ZHANG, Wei QI

Sayfa
152–158
DOI
—

Abstract

In this paper, we say a ring $R$ is Nil$_{\ast}$-Artinian if any descending chain of nil ideals stabilizes. We first study Nil$_{\ast}$-Artinian properties in terms of quotients, localizations, polynomial extensions and idealizations, and then study the transfer of Nil$_{\ast}$-Artinian rings to amalgamated algebras. Besides, some examples are given to distinguish Nil$_{\ast}$-Artinian rings, Nil$_{\ast}$-Noetherian rings and Nil$_{\ast}$-coherent rings.