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 right coset of $A$ by $m$ is
\[Am = \{am : a\in A\}.\]We define the quotients
\[\begin{align*} M/A &= \{mA : m\in M\}; \\ M\backslash A &= \{Am : m\in M\}. \end{align*}\]$M/A$ is also read as $M$ mod $A$.
Let $M$ be an abelian magma and $A$ be a submagma. For any $m\in M$,
\[mA = Am,\]and therefore
\[M/A = M\backslash A.\]