Abstract
In this paper we give some characterization of minimal distributive semi lattice and proper filter in directed above semi lattice. Also this manuscript illustrates several principal results concerning congruence kernels of minimal distributive semi lattice S and provides a necessary and sufficient condition for a semi lattice congruence ≡ on Sis a * congruence. And also established a necessary and sufficient condition of an ideal of minimal distributive semi lattice S is a kernel ideal of semi lattice S.
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