Definition:Identity/Also known as
Jump to navigation
Jump to search
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