It is proved that the ad joint semigroup of a positive implicative BCKalgebra with condition(s) is a lower semilattice.
本文讨论了正蕴涵BCK－代数的剩余刻划；证明了具有条件（S）的正蕴涵BCK－代数的伴随半群是一个下半格。
In this paper,the author discusses the structure of π-left zero semi-groups,to prove that if S is a finite π-left zero semi-groups such that |E(s)|≤4,then the lattice of congruences C(S) of S is a semi-modular lattice.
通过研究π-左零半群的结构,利用所得的结论证明:若S是有限π-左零半群|E(s)|≤4,则C(S)是半模格。