Nil$_{\\ast}$-Artinian rings

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International Electronic Journal of Algebra
Volume:34 Issue:34
Nil$_{\\ast}$-Artinian rings

Nil$_{\\ast}$-Artinian rings

Authors : Xiaolei ZHANG, Wei QI

Pages : 152-158

Doi:10.24330/ieja.1260486

View : 32 | Download : 33

Publication Date : 2023-07-10

Article Type : Research Paper

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.
Keywords : Nil \\ast Artinian ring, idealization, amalgamated algebra

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