格蕴涵代数和MTL-代数中的超LI-理想
Ultra LI-ideals in lattice implication algebras and MTL-algebras
摘要：
指出了格蕴涵代数的超\textit{LI} -理想的一个错误，给出了\textit{LI} -理想是超\textit{LI} -理想的一些新的充必要条件.此外，将\textit{LI} -理想的概念推广到MTL-代数，引入了MTL-代数的（素，超，固执，布尔）\textit{LI} -理想和\textit{ILI} -理想，给出了一些重要的例子，并证明了下列概念在MTL-代数中是等价的：（1）素真\textit{LI} -理想与布尔\textit{LI} -理想，（2）素真\textit{LI} -理想与\textit{ILI} -理想，（3）真顽固\textit{LI} -理想，（4）超\textit{LI} -理想.
英文摘要：
A mistake concerning the ultra \textit{LI}-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an \textit{LI}-ideal to be an ultra \textit{LI}-ideal are given. Moreover, the notion of an \textit{LI}-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) \textit{LI}-ideal and an \textit{ILI}-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper \textit{LI}-ideal and Boolean \textit{LI}-ideal, (2) prime proper \textit{LI}-ideal and \textit{ILI}-ideal, (3) proper obstinate \textit{LI}-ideal, (4) ultra \textit{LI}-ideal.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
