Characterization of Distributive and Standard Ideals in Semilattices
AbstractThis 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. Keywords: Distributive ideal, Distributive semilattice, Dually Distributive ideal, Standard ideal, Join Semi Lattice.
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