A pre A*-algebra is the algebraic form of the 3-valued logic. In this paper, we define a binary operation on pre A*-algebra and show that is a semilattice. We also prove some results on the partial ordering which is induced from the semilattice. We derive necessary and sufficient conditions for pre A*-algebra (A,Ù,Ú, (-)~) to become a Boolean algebra in terms of this partial ordering and binary operation and also find the necessary conditions for (A , ) as a lattice.
Key words: Pre A*- algebra, poset, semilattice, centre, Boolean algebra.
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