A note of implicative semilattices
Zhu Shao-ping · Basic Sciences Journal of Textile Universities · 2006
A minimal base of implicative semilattices is given.Let L be nonempty set,∧ and * two binary operations,and 1 is a constant element of L.Then(L;∧,*,1) is an implicative semilattices if and only if it satisfies the follow:(1)(y*z)*((z*x)*(y*x))=1,(2)(x*y)*((y*x)*x)=(y*x)*((x*y)*y),(3) x*(y*z)=(x∧y)*z,(4)(y*1)*x=x.As a consequence of the above result,we have that implicative semilattices form an algebraic variety.