# Identity element

From Encyclopedia of Mathematics

*neutral element*, *unit 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.

**How to Cite This Entry:**

Identity element.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Identity_element&oldid=35633