冪零元與局部冪零理想

On nilpotent elements and locally nilpotent ideals

李詔琦(Shao-Chi Lee)

指導教授 ： 李白飛 教授

國立臺灣大學/理學院/數學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201600882

摘要

經由2-primal ring及NI ring的拓撲結構，我們研究一種新的類型的環，滿足所有冪零元形成一個局部冪零理想，並稱之為NL ring。本文首先介紹NL ring的基本性質，接著研究NL ring和局部強質理想之間的關係，最後，探討NL ring下的拓樸結構。

關鍵字

局部冪零理想 ； Levitzki radical ； L 正規 ； lspm, NL 環 ； 局部強質理想

並列摘要

Motivated by 2-primal rings, NI rings and their associated topological structures, we consider a new class of rings, NL rings, in which the nilpotent elements form a locally nilpotent ideal. We first introduce some basic properties of NL rings, and then study the relationships between NL rings and locally strong prime ideals. Lastly, we give the topological structures induced by NL rings.

並列關鍵字

locally nilpotent ideal ； Levitzki radical ； L-normal ； lspm ； NL ring ； locally strong prime ideal

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