Does the abelian group in the definition of a left R-module need to be additive?

Question

Let $R$ be an arbitrary ring and $M$ an abelian group, a left $R$ module consists of the aforementioned abelian group $M$ and an operation $f:R \times M\rightarrow{M}$ satisfying for $r,s\epsilon{R}$ and $x,y\epsilon{M}$

$r(x+y)=rx+ry$

$(r+s)x=rx+sx$

$(rs)x=r(sx)$

$1_{R}x=x$ if $R$ is unital

The Wikipedia article uses the notation $(M,+)$ for $M$ and the encyclopedia of mathematics page explicitly says that $M$ is additive while other sources make no mention of the binary operation in $M$. So does $M$ need to be additive or can it be multiplicative?