格蕴涵代数中的极小素理想及α-理想  

Minimal prime ideals and α-ideals in lattice implication algebras

作　　者：孟彪龙[1] 付巧峰[1] 梁少辉[1] MENG Biaolong;FU Qiaofeng;LIANG Shaohui(Department of Mathematics,Xi＇ an University of Science and Technology,Xi＇ an 710054,China)

机构地区：[1]西安科技大学数学系,西安710054

出　　处：《计算机工程与应用》2018年第16期44-48,92,共6页Computer Engineering and Applications

基　　金：西安科技大学博士启动基金(No.2016QDJ050);陕西省教育厅专项基金(No.17JK0510)

摘　　要：在格蕴涵代数中,证明了极小素理想与极小格素理想的等价性,继而给出了极小素理想与零化子的相互表示定理。提出了格蕴涵代数中的α-理想概念并给出其若干等价刻画,证明了极小素理想是α-理想。证明了全体素α-理想之集S_α(L)是一个紧的Stone空间,进一步给出S_α(L)分别是T_1、T_2拓扑空间的充要条件。The equivalence of minimal prime ideals and minimal lattice prime ideals in lattice implication algebras is proved,then the reciprocal representation theorem of minimal prime ideals and annihilators is provided.The concept ofα-ideal is proposed and several equivalent characterizations are established,also prime ideals being α-ideals are proved.The set Sα（L） of all prime α-ideals being a compact Stone space is proved,moreover the sufficient and necessary conditions for Sα（L） being T1,T2 spaces respectively are obtained.

关 键 词：极小素理想 零化子 α-理想 拓扑空间 

分 类 号：O15[理学—数学]