零$_｛\ast｝$-阿蒂尼安环

IF 0.5 Q3 MATHEMATICS

International Electronic Journal of Algebra Pub Date : 2023-03-05 DOI:10.24330/ieja.1260486

Xiaolei Zhang, W. Qi

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引用次数: 0

摘要

在本文中，我们说一个环$R$是Nil$_｛\sast｝$-Artinian，如果零理想的任何下降链稳定。我们首先从商、局部化、多项式扩展和理想化的角度研究了Nil$_｛\ast｝$-Artinian性质，然后研究了Nil$_。此外，还给出了一些例子来区分Nil$_｛\ast｝$-Artinian环、Nil$_{\ast｝$-Noetherian环和Nil$-{\ast}$-相干环。

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Nil$_{\ast}$-Artinian rings

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.

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来源期刊

International Electronic Journal of Algebra MATHEMATICS-

CiteScore

0.90

自引率

16.70%

发文量

审稿时长

36 weeks

期刊介绍： The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.