2 . the structure of the lattice implication sub - algebra which generated from a subset , and the product of lattice implication algebra were studied . the necessary condition was given of a lattice implication algebra which can be decomposed into lattice implication algebra ' s product . it is proved that lattice h implication algebra is a boole ring with a unit 2 、对格蕴涵代数中由一子集生成的格蕴涵子代数的结构及格蕴涵代数的直积进行了研究，给出了一格蕴涵代数可分解成一族格蕴涵代数直积的必要条件，证明了格h蕴涵代数是一有单位元的布尔环。
Finally , this paper introduces the concepts of subl - cusl , algebraic subl - domain , l - cusl embedding and projection pair for domains . making use of the representation theorem for algebraic l - domains , this paper proves that the category of algebraic l - domains with projection pairs for domains as morphisms is eqivalent to the category of l - cusls and l - cusl embeddings 最后，本文引入了子l - cusl ，子代数l - domain ， l - cusl嵌入和domain上的投射对等相关的几个概念，并通过代数l - domain的表示定理证明了以l - cusl为对象， l - cusl嵌入为态射的范畴lcusl ~ *与以代数l - domain为对象， domain上的投射对为态射的范畴aldom ~ *是等价的两个范畴。
In section 2 . 2 , we prove that if the set of arrows in a quiver is not empty , then nq is not semisimple . we construct the nonsovable subalgebra of nq when there is no less than one circle whose length is bigger than one , and there is no loop in quiver q , thus leads to a conclusion that nq is nonsovable . using the index arrays to discuss the operation of necklace word . construct a sovable subalgebra of nq , which is not nilpotent . this shows that nq is not nilpotent provided that there is a cyclic with length bigger than 1 当箭图中有长度大于1的循环，且无圈时，构造了n _ q的非可解子代数，从而证明了n _ q是不可解李代数。我们还利用指标数组讨论了项链字的运算，构造了n _ q的可解非幂零子代数，从而证明了当箭图中有长度大于1的循环时，项链李代数非幂零。在2
