TITLE: Definition of "fixed point" for binary operator
QUESTION [2 upvotes]: What is a term for a value $x \in X$ that for binary operator $f\colon X\times X \to X$ maps always to itself, no matter what is the other value
$$
\forall y \in X \quad f(x, y) = f(y, x) = x
$$
Is it called "fixed point" too or not?
Examples are $0$ for numbers multiplication, $\mathrm{false}$ for conjunction, $\mathrm{true}$ for disjunction, $\emptyset$ for intersection, etc.

REPLY [1 votes]: Such elements are often called absorbing elements. In semigroup theory it is often called the identity or zero element.
see:
https://en.wikipedia.org/wiki/Absorbing_element
https://www.encyclopediaofmath.org/index.php/Absorbing_element
https://planetmath.org/absorbingelement
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