Remark

Let $E$ be a magma with law denoted by $\tau$. It should be noted that a subset $A$ of $E$ which is stable under the left action on $E$ on itself is not necessarily stable under the right action of $E$ on itself; a subset $A$ of $E$ stable under the left (resp. right) action of $E$ on itself is stable under the law on $E$ but the converse is not in general true. More precisely, $A$ is stable under the law on $E$ if and only if $A \tau A \subset A$ whereas $A$ is stable under the left (resp. right) action on $E$ on itself if and only if $E \tau A \subset A$ (resp. $A \tau E \subset A$).