• IDEALS IN ALMOST SEMILATTICE

Abstract

The concept of ideal in an Almost Semilattice  is introduced and the smallest ideal containing a given nonempty subset of an  is described. Also, several properties of ideals are derived. Proved that the set I (L), of all ideals in an  L, is a distributive lattice and also, the set PI (L), of all principal ideals form semilattice is established. Derived set of equivalent identities for the intersection of any family of ideals is again an ideal and a 1-1 correspondence between ideals (prime) of and ideals (prime) PI (L) is established. Finally obtained, every amicable set in is embedded in a semilattice PI (L).