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高校应用数学学报
高校应用数学学报  2015, Vol. 30 Issue (4): 445-456    
    
否定非对合剩余格的LI-理想理论
刘春辉
赤峰学院 数学与统计学院, 内蒙古赤峰 024001
LI-ideals theory in negative non-involutive residuated lattices
LIU Chun-hui
Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, China
 全文: PDF 
摘要： 综合运用泛代数和格序理论的方法和原理研究否定非对合剩余格的理想问题. 首先, 在否定非对合剩余格$L$中引入LI-理想以及由$L$的非空子集生成的LI-理想的概念并考察它们的相关性质. 其次, 在$L$的全体LI-理想之集$\textbf{Id}(L)$上定义了格运算$\sqcap$和$\sqcup$, 证明了$(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$构成一个分配的连续格, 从而构成一个Frame. 然后, 在$L$中引入素LI-理想概念并讨论其性质, 建立了预线性否定非对合剩余格的素LI-理想定理. 最后, 借助于素LI-理想之特性获得了预线性否定非对合剩余格的LI-理想格$(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$中素元的若干等价刻画.
关键词： 否定非对合剩余格;  LI-理想;  素LI-理想;  代数格;  连续格;  素元    
Abstract: In this paper, the problem of ideals in negative non-involutive residuated lattices is studied by using the principle and method of universal algebras and lattice-order theory. Firstly, the notions of LI-ideals and LI-ideal generated by a non-empty subset are introduced in negative non-involutive residuated $L$, and some their properties are investigated. Secondly, lattice operations $\sqcap$ and $\sqcup$ are defined on the set $\textbf{Id}(L)$ of all LI-ideals in $L$. It is proved that $(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$ forms a distributive continuous lattice, and particularly forms a frame. Then, the notion of prime LI-ideals is introduced in $L$ and its properties are discussed. The prime LI-ideals theorem is estabLIshed in pre-LInear negative non-involutive residuated lattices. Finally, some equivalent characterizations of prime elements of LI-ideal lattice $(\textbf{Id}(L), \subseteq, \sqcap, \sqcup)$ are obtained by means of prime LI-ideals in pre-LInear negative non-involutive residuated lattice $L$.
Key words: negative non-involutive residuated lattice    LI-ideal    prime LI-ideal    algebraic lattice    continuous lattice    prime element
收稿日期: 2014-11-23 出版日期: 2018-05-19
CLC:  O141.1  
基金资助: 国家自然科学基金(60774073); 内蒙古自治区高等学校科学研究项目(NJSY14283)
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引用本文:

刘春辉. 否定非对合剩余格的LI-理想理论[J]. 高校应用数学学报, 2015, 30(4): 445-456.

LIU Chun-hui. LI-ideals theory in negative non-involutive residuated lattices. Applied Mathematics A Journal of Chinese Universities, 2015, 30(4): 445-456.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2015/V30/I4/445

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