0-Distributive and P-Uniform Semilattices

Abstract

AbstractA counter-example is provided to the conjecture of Y. S. Pawar and N. K. Thakare that a semilattice S with 0 is 0-distributive if and only if for each filter F and each ideal I such that F ∩ I = Ø, there exists a prime filter containing F and disjoint from I. This shows that 0-distributivity is not equivalent to weak distributivity. A characterization is also given of finite P-uniform semilattices in terms of 0-distributivity.