Study on Distributive Lattice and Boolean Function

Abstract

In this thesis the nature of distributive lattice and Boolean function is studied. Distributive lattices have played many roles in the development of lattice theory. Distributive lattices have been studied by several authors including Abbott [6], Cornish [17], Nieminen [10].A poset (L,£) is said to form a lattice if for every a,bÎL if sup{a,b} and inf{a,b} exist in L . A lattice L is said to be distributive if "a,b,cÎ L , a Ù (b Ú c) = (a Ù b) Ú (a Ù c) holds. In this thesis we give several results on distributive lattice and Boolean function which will certainly extend and generalize many results in lattice theory. We have proved that N ´ N is modular where N is the chain of naturals under usual £ . We also generalize the following theorem of L.Nachbin[16], let L be a distributive lattice with 0 and 1 then L is Boolean iff all its prime ideals are unordered by set inclusionÍ.