Volume 37 • Number 3 • 2014   • Some Characterizations of 0-Distributive Semilattices H. S. Chakraborty and M. R. Talukder Abstract. In this paper we discuss prime down-sets of a semilattice. We give a characterization of prime down-sets of a semilattice. We also give some characterizations of $0$-distributive semilattices and a characterization of minimal prime ideals containing an ideal of a $0$-distributive semilattice. Finally, we give a characterization of minimal prime ideals of a pseudocomplemented semilattice. 2010 Mathematics Subject Classification: 06A12, 06A99, 06B10 Full text: PDF