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...Pacific journal of mathematics vol no semigroups whose lattice congruences is boolean howard hamilton and thomas nordahl the commutative forms a are determined they i null order two or less ii discrete trees iii groups which direct sum prime cyclic in factors have same iv one element inflation dis crete tree v free product with zero semigroup type amal gamated over trivial vi introduction this paper semilattice will be considered to an upper e forzyxwvutsrqponmlkjihgfedcbazyxwvutsrqponmlkjihgfedcba x yes we y if only xy say that s for all es interval z finite chain any let l denote t subsemigroup there exists function satisfying restriction identity mapping f then said shall terms not defined may found now present some results needed our proofs theorem jaers greatest semi decomposition...