A Note on Complete Boolean Algebras

1. Introduction. Among commutative rings, Boolean algebras stand just below fields in simplicity of structure. In contrast, little is known concerning their classification. The purpose of this paper is to present a decomposition theorem for complete Boolean algebras, which, in a small way, simplifies the classification problem. As an illustration of how this decomposition theorem can be used, it is shown that an infinite cardinal number ^ can be the power of a complete Boolean algebra if and only if b$N° = fc$. The words "complete Boolean algebra" will henceforth often be abbreviated C.B.A. Similarly, B.A. stands for Boolean algebra. The join, meet and complement operations in a B.A. are denoted Vi