Definition 1. A magma is a structure $(M, *)$ where $M$ is a set and $*$ is a binary operation under which $M$ is closed, i.e. for all $a$, $b \in M$,
\[a * b \in M.\]Definition 2. Let $(M, *)$ be a magma. If $*$ has a certain property, then we may also say $M$ has this property. For example, $M$ is associative if $*$ is associative.
Specially, we call a magma abelian if it is commutative.