Name of property that $0 \cdot x = 0$

Question

What's the name of the property that $0 \cdot x = x \cdot 0 = 0$ for all $x \in \mathbb{R}$?

I suppose it would be some group theoretic name but I can't recall it and I've searched everywhere, it wouldn't be the identity nor an inverse, so I'm at a loss.

A look at the comments on this might help. – drhab Nov 19 '15 at 10:24 — drhab, Nov 19 '15 at 10:24

score 1 · Answer 1 · answered Nov 19 '15 at 10:09

1

$0$ is an absorbing element (for the multiplication) (Wikipedia) Synonyms are zero element and annihilating element. (Note that a non-trivial group can never have an absorbing element!)

answered Nov 19 '15 at 10:09

Myself

8,987

1

I suggest another name: killer element. (not to be confused with Killing form.) ;) – Martin Brandenburg Nov 19 '15 at 10:17
@MartinBrandenburg Best not to use that term while waiting in line at the airport though in these days of nervosity :-) – Myself Nov 19 '15 at 10:28

score 0 · Answer 2 · answered Nov 19 '15 at 10:15

There are actually at least two properties involved here.

Commutative nature of multiplication: $a.b = b.a$
Multiplication has an annihilating element (let's call it $A$): $A.x = A$

By using (1.) and (2.), one gets: $A.x = x.A = 0$. The fact that $A$ is $0$ is another sub-theory.

Name of property that $0 \cdot x = 0$

2 Answers2