SOME CHARACTERIZATIONS OF 0-DISTRIBUTIVE SEMILATTICES
Himadri Shekhar Chakraborty, M. R. Talukder · 2012
In this paper we discuss prime down-sets of a semilat- tice. 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. Semilattices have been studied by many authors. The class of dis- tributive semilattices is an important subclass of semilattices. We refer the readers to (4, 9, 10) for distributive semilattices. We also refer the monograph (5) for the background of distributive semilattices. The class of 0-distributive semilattices is a nice extension of the class of distributive semilattices. This extension is useful for the study of pseu- docomplemented semilattices. For pseudocomplemented semilattices we refer the readers to (2, 3, 5, 6). We also refer the readers to (7, 8) for 0-distributive semilattices (see (1, 11) for 0-distributive lattices). In this paper we study 0-distributive semilattices. By semilattice we mean meet-semilattice.