Boolean Powers of Abelian Groups

where (f + g)(u) = V_,,+,,,f(v) A f(w). Since E is countable, ZcB) can be defined for any countably complete Boolean algebra (ccBa) B where Z is the group of the integers. This kind of group was first (1962) studied by Balcerzyk [l]. However, it seems that not much attention was paid to such groups for a rather long period. Under the point of view in [l, Theorem 51 and [13, Proposition 11, it can be said that there has been studies about it after around 1980 [5-18,24,29,30]. In the present paper we investigate cotorsion-freeness and algebraical compactness of Boolean powers. Undefined notions about abelian groups and Boolean algebras are the usual ones and can be found in [20] and [23] respectively. All groups in this paper are abelian groups.