格蕴涵代数的LI-理想格及其素元刻画  

LI-ideals lattice and its prime elements characterizations in a lattice implication algebra

作　　者：刘春辉[1] 

机构地区：[1]赤峰学院数学与统计学院,内蒙古赤峰024001

出　　处：《高校应用数学学报（A辑）》2014年第4期475-482,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10371106;60774073)

摘　　要：运用格理论的原理和方法对格蕴涵代数L的LI-理想概念作进一步研究.首先,在L的全体LI-理想之集ф_(LI)(L)上定义了格运算■和■,蕴涵运算■以及伪补运算■,证明了(ф_(LI)(L),,■,■,■,{O},L)构成一个完备Heyting代数的结论.其次,利用运算固的性质给出了(ф_(LI)(L),,■,■,■,■,{O},L)成为Boolean代数的若干充要条件.最后,借助于L的素LI-理想之特性获得了格(ф_(LI)(L),,■,■,{O},L)中素元的若干等价刻画.The concept of LI-ideals in lattice implication Mgebras L was further studied by using the principle and method of lattice theory. Firstly, the lattice operations and , implication operation and pseudo-complement operation are defined on the set фLI（L） which contains all LI-ideals in L, and фLI（L）, {O}, L） is proved to form a complete Heyting algebra. Secondly, some necessary and sufficient conditions of фLII（L）, , {O}, L） becoming a Boolean algebra are given by using properties of operation . Finally, some equivalent characterizations of prime elements in lattice фLI（L）, {O}, L） are obtained by means of prime LI-ideals in L.

关 键 词：格值逻辑 格蕴涵代数 LI-理想 完备Heyting代数 Boolean代数 素元 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]