Let $M$ be a magma, $A$ be a submagma and $m \in M$.
The left coset of $A$ by $m$ is
\[mA = \{ma : a \in A\}.\]The left coset quotient of $M$ by $A$ is
\[M / A = \{mA : m \in M\}.\]The right coset of $A$ by $m$ is
\[Am = \{am : a \in A\}.\]The right coset quotient of $M$ by $A$ is
\[M \backslash A = \{Am : m \in M\}.\]
Let $M$ be an abelian magma and $A$ be a submagma. For any $m \in M$,
\[mA = Am,\]and hence
\[M / A = M \backslash A.\]