  In \cite{AB}, the dagger closure is extended over finitely generated modules
over Noetherian local domain $(R,\fm)$ and it is proved to be a Dietz closure.
In this short note we show that it also satisfies the `Algebra axiom' of
\cite{R.G} and this leads to the following result of this paper: For a complete
Noetherian local domain, if it is contained in an almost Cohen-Macaulay domain,
then there exists a balanced big Cohen-Macaulay algebra over it.
