A Completion of Semi-simple MV-algebra

The notion of MV-algebra was introduced by C.C. Chang in 1958 to provide an algebraic proof of the completeness of Lukasiewicz axioms for infinite valued logic. These algebras appear in the literature under different names: Bricks, Wajsberg algebra, CN-algebra, bounded commutative BCK-algebras, etc. The purpose of this paper is to give a topological lattice completion of semisimple MV-algebras. To this end, we characterize the complete atomic center MV-algebras and semisimple algebras as subalgebras of a cube. Then we define the <TEX>$delta$</TEX>-completion of semisimple MV-algebra and construct the <TEX>$delta$</TEX>-completion. We also study some important properties and extension properties of <TEX>$delta$</TEX>-completion.