Boolean Algebras of Elementary Characteristic $(1,0,1)$ with the Computable Set of Atoms and the Ideal of Atomic Elements

The problem considered in this paper is somehow more general then the investigation of relations between $n$-computability and decidability of Boolean algebra of elementary characteristic $(n,0,1)$ which is complete. In this paper we consider computable Boolean algebra of elementary characteristic $(1,0,1)$ with the computable set of atoms and the ideal of atomic elements. We prove that every such Boolean algebra has strongly computable isomorphic copy. We also generalize this result to Boolean algebras of elementary characteristics $(n,0,1)$.