蕴涵格、弱R_o代数与正则剩余格  

Implication lattices, weak R_o-algebras and regular residauted lattices

作　　者：苏忍锁[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721007

出　　处：《宝鸡文理学院学报（自然科学版）》2004年第2期89-91,119,共4页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

摘　　要：讨论了蕴涵格、弱Ro代数以及正则剩余格之间的相互关系,证明了以下结论:(1)弱Ro代数既是蕴涵格又是正则剩余格;(2)蕴涵格L是正则剩余格(弱Ro代数)的充分必要条件是:对任意x,y,z∈L,x→(y→z)=y→(x→z);(3)正则剩余格L是蕴涵格(弱Ro代数)的充分必要条件是:对任意x,y,z∈L,x→y∨z=(x→y)∨(x→z)。The mutual relations among implication lattices, weak R_o-algebras and regular residauted lattices are discussed,and the following conclusions are testified: (1) weak R_o-algebras is both implication lattices and regular residauted lattices; (2) the necessary and sufficient conditions under which a implication lattice L becomes a regular residauted lattice or a weak R_o-algebra is the following holds for all x,y,z∈L,x→(y→z)=y→(x→z); (3) the necessary and sufficient conditions under which a regular residauted lattice becomes a implication lattice or a weak R_o-algebra is the following holds for all x,y,z∈L,x→y∨z=(x→y)∨(x→z).

关 键 词：蕴涵格 弱R0代数 正则剩余格 

分 类 号：O141.1[理学—数学]