Identity element

neutral element, zero element

An element of an algebraic structure $S$, often denoted $1$, $I$ or $e$, with a specific property with respect to a binary operation $*$: $$ \forall x \in S \ \ 1 * x = x * 1 = x\ . $$

Where the binary operation is written additively, the identity element may be denoted $0$ or $O$, and termed a zero element.