Associative

Definition

Let $(A,\ast )$ be a binary magma on a set $A$. Say $\ast$ is associative iff $x\ast (y\ast z)=(x\ast y)\ast z$ for all $x,y,z\in A$.

Remarks

• In the presence of an assumption of associativity, we can write $x_0\ast x_1\ast \cdots \ast x_{n-1}$ without parentheses.