Some Properties of the congruences of a Near lattice


Mizanur Rahman,A.S.A.Noor ,



near lattice,semi lattice ,congruences ,ideals,


By a near lattice we mean a meet semi lattice with the property that any two elements possessing a common upper bound, have a supremum. In this paper, we have studied some properties of congruences in near lattices. For a near lattice S, if n is an upper and neutral then the set of all finitely generated n-ideals )S(Fnis a lattice. Here we have provided an isomorphism between the lattice of congruences ))S(F(Cn and )S(C.We also showed that if n is a central element of a distributive near lattice S, then ))S(F(I)S(Inn≅If and only if )S(Fn is generalized Boolean, where )S(In is the lattice of all n-ideals of S. Finally we include some equivalent conditions for the permutability of the smallest congruences )I(Θ containing the n-ideals I, when S is a distributive medial near lattice and n is an upper element.


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