Module algebra
= Module algebra
{title2=$h(ab)=\sum(h_{(1)}a)(h_{(2)}b)$}
An <algebra over a field> acted on by a <bialgebra> is a module algebra when multiplication and unit are <module> maps: the displayed product identity holds and $h1=\varepsilon(h)1$. This expresses the product rule determined by <comultiplication>.