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

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?

• We have $0\cdot a=a\cdot 0=0$ for all $a\in R$. "0" is just the null-element of the ring R. Mar 21, 2020 at 16:18
• If you are assuming a ring or a field the only such element is the additive identity and it is just called "$0$" (As by distribution $0\times a = (0+0)\times a = 0\times a + 0\times a$ so $0\times a$ must but equal to $0$. And it is unique as $n=n*a=n*(a+a)=n*a+n*a=n+n$ so $n=0$.) But for abstract structures that need not be rings or fields then .... Well, Ben Steffan answer has the word for it. Mar 21, 2020 at 16:27
• @Peter Well, to be fair the OP never stated we were working with a Ring. S/he wanted the name for such an element with any binary operation on a set. Mar 21, 2020 at 16:33