Characterization of Distributive and Standard Ideals in Semilattices

This paper investigates the concepts of distributive ideal, dually distributive ideal and standard ideal in a join semilattice. It concerns with the property of ideals in a distributive semilattice. We obtain a characterization theorem for distributive (dually distributive) and standard ideal in a join semilattice. We establish the necessary and sufficient condition for a distributive ideal to be standard ideal. Finally, we bear out the fundamental theorem of homomorphism and Isomorphism theorem of standard ideal.