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.

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characteristic

Noun

  1. a distinguishable feature of a person or thing
  2. the integer part of a logarithm
  3. the distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc)
  4. 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.

Adjective

  1. 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.

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