Lattice in Pre A*-Algebra

This study is on algebraic structure of Pre A*-algebra. First we recall partial ordering = on Pre A*-algebra and recall that Pre A*-algebra as a Poset. We recall if A is a Pre A*-algebra then (A, =) is a lattice. We define (for any subset L of a Pre A*-algebra) a lattice (L, ?, ?) in a Pre A*-algebra. We define semi lattice, sub lattice and bound elements, bounded lattice, distributive lattice, modular lattice, atoms, dual atoms, irreducible elements in a Pre A*-algebra. We define Pre A*-homomorphism and we prove representation theorem in Pre A*-Algebra also we prove f: A ? P (B) is an isomorphism.