## CHARACTERISTIC

### Characteristic

In mathematics, the**characteristic**of a ring

*R*, often denoted char, is defined to be the smallest number of times one must use the ring's multiplicative identity element in a sum to get the additive identity element ; the ring is said to have characteristic zero if this sum never reaches the additive identity.

*The above text is a snippet from Wikipedia: Characteristic (algebra)*

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### characteristic

#### Noun

- a distinguishable feature of a person or thing
- the integer part of a logarithm
- the distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc)
- The minimum number of times that the unit of a field must be added unto itself in order to yield that field's zero, or, if that minimum natural number does not exist, then (the integer) zero.
- A field's characteristic, if non-trivial, must be prime, otherwise the field would not be an integral domain, which fields must be. For example, if a field's characteristic were six, then (1+1)+(1+1)+(1+1) = 0; if 1+1 were labeled
*A*and 1+1+1 were labeled*B*, then*A*+*A*+*A*= 0,*A*(1 + 1 + 1) = 0 by distributivity;*A**B*= 0, and the field could not be an integral domain.

- A field's characteristic, if non-trivial, must be prime, otherwise the field would not be an integral domain, which fields must be. For example, if a field's characteristic were six, then (1+1)+(1+1)+(1+1) = 0; if 1+1 were labeled

#### Adjective

- Being a distinguishing feature of a person or thing.

*The above text is a snippet from Wiktionary: characteristic*

and as such is available under the Creative Commons Attribution/Share-Alike License.

and as such is available under the Creative Commons Attribution/Share-Alike License.