A Completion of Semi-simple MV-algebra

Abstract

We first show that any complete MV -lgebra whose Boolean subalgebraof idempotent elements is atomic, called a complete MV -algebra with atomic center, isisomorphic to a product of unit interval MV -algebra I’s and finite linearly ordered MV -algebras of A(m)-type (m 2 Z+). Secondly, for a semi-simple MV -algebra A, we introduce a completion ±(A) of A which is a complete, MV -algebra with atomic center. Under their intrinsic topologies (see x3) A is densely embedded into ±(A): Moreover, ±(A) has the extension universal property so that complete MV -algebras with atomic centers are epireflective in semi-simple MV -algebras