Sectionally Pseudocomplemented Distributive Nearlattices

Abstract

This thesis studies the nature of a sectionally pseudocomplemented distributive nearlattice. By a nearlattice S we will always mean a meet semilattice together with the property th9.t any two elements possessing a common upper bound, have a supremum. Cornish and Hickman in their paper [14] referred this property as the upper bound property, and a semdattice of this nature as a semilattice with the upper bound property. Cornish and Noor in [15] preferred to call these semilattices as nearlattices, as the behaviour of such a semilattice is closer to that of a lattice than an ordinary semilattice. Of course a nearlattice with a largest element is a lattice. So the idea of pseudocomplementation is not possible 1n case of a general nearlattice. But for a nearlattice with a smallest element we can talk about sectionally p s eud ocom plemen ted nearlattice. Moreover, we can discuss on relatively p seudocom plemen ted nearlattices. In this thesis, we give several results on sectionally (relatively) pseudocomplemented nearlattices which certainly extend and generalize many results 1n lattice theory. ----------