In the draft of my book there was an error. I’ve corrected it today.

Wrong: $latex \forall a, b \in \mathfrak{A}: ( \mathrm{atoms}\, a \sqsubset \mathrm{atoms}\, b \Rightarrow a \subset b)$.

Right: $latex \forall a, b \in \mathfrak{A}: ( a \sqsubset b \Rightarrow \mathrm{atoms}\, a

\subset \mathrm{atoms}\, b)$.

There are the same error in my article Filters on posets and generalizations, International Journal of Pure and Applied Mathematics, 74, No. 1 (2012), 55-119.