# Definition:Identity/Also known as

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## Identity: Also known as

Other terms which are seen that mean the same as **identity** are:

**Two-sided identity**, to reflect the fact that it is both a left identity and a right identity.**Neutral element**, which is perfectly okay, but considered slightly old-fashioned.**Unit element**, but this is not recommended as it is too easy to confuse it with a unit of a ring.**Unity**, but this is generally reserved for a ring unity or unity of field, and can also mean the number $1$.**Zero**, but it is best to reserve that term for a zero element.- The
**trivial element**, in the context of a group.

The symbols used for an **identity element** are often found to include $0$ and $1$. In the context of the general algebraic structure, these are not recommended, as this can cause confusion.

Some sources use $I$ for the **identity**.

## Sources

- 1965: J.A. Green:
*Sets and Groups*... (previous) ... (next): $\S 4.3$. Units and zeros - 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): Chapter $\text I$: Algebraic Structures: $\S 4$: Neutral Elements and Inverses - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**group** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**group**