# Null element of a binary operation

For a binary (commutative) operation $$*$$ over a set $$S$$ the identity element is an element $$i\in S$$ such that $$\bigl(\forall x\in\ S \bigr)\bigl(i*x=x\bigr)$$ Is it correct/common to call an element $$a\in S$$ such that $$\bigl(\forall x\in\ S \bigr)\bigl(a*x=a\bigr)$$ the null element?

Well, the zero element $$0$$ of a ring $$R$$ is absorbing, i.e., $$r0 = 0 =0r$$, since $$r0 = r(r+(-r)) = r^2 - r^2=0$$. So maybe absorbing is the notion looked for here.