In an algebraic system, is there a general name for an element that behaves like 0 does for multiplication in $\mathbb R$?

Question

In an algebraic system, an element that behaves like $0$ does for addition or like 1 does for multiplication of real numbers is called an " identity element" ; an element that is to some element $a$ like $\frac 12$ is to 2 is called an inverse element of $a$.

Is there a general name for an element that behaves like $0$ does for multiplication?

I mean, a general name for an element $n$ having this property : $ \forall(a) a * n = n*a=n$ , $*$ being a binary operation?

Answer 1

Yes, such an element is known as an absorbing element.