Does the following property of the composition of a magma have a name?

Question

If $M$ is a magma and

$$+:M\times M\to M$$

is its law of composition, does the property

$$(x+y)+z=x+(y+z)\qquad\forall\ x,y,z\in M :\quad y\neq x,z$$

have a name? It resembles the associativity of the law, with the denoted exceptions.