理學院: 數學研究所指導教授: 李白飛 教授李詔琦Lee, Shao-ChiShao-ChiLee2017-03-062018-06-282017-03-062018-06-282016http://ntur.lib.ntu.edu.tw//handle/246246/276759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。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.389178 bytesapplication/pdf論文公開時間: 2016/7/26論文使用權限: 同意有償授權(權利金給回饋學校)局部冪零理想Levitzki radicalL 正規lspm, NL 環局部強質理想locally nilpotent idealL-normallspmNL ringlocally strong prime idealthesis10.6342/NTU201600882http://ntur.lib.ntu.edu.tw/bitstream/246246/276759/1/ntu-105-R03221001-1.pdf