Definition of "characteristic" in English

adjective

1. Being a distinguishing feature of a person or thing.

noun

1. A distinguishing feature of a person or thing, a part of mental or physical behavior.

2. (mathematics) The integer part of a logarithm.

3. (nautical) The distinguishing features of a navigational light on a lighthouse etc by which it can be identified (colour, pattern of flashes etc.).

4. (algebra, field theory, ring theory) For a given field or ring, a natural number that is either the smallest positive number n such that n instances of the multiplicative identity (1) summed together yield the additive identity (0) or, if no such number exists, the number 0.

   • The characteristic of a field, if non-zero, must be a prime number.
   • 1962 [John Wiley & Sons], Nathan Jacobson, Lie Algebras, 1979, Dover, page 289, In this chapter we study the problem of classifying the finite-dimensional simple Lie algebras over an arbitrary field of characteristic 0.
   • 1992, Simeon Ivanov (translator), P. M. Gudivok, E. Ya. Pogorilyak, On Modular Representations of Finite Groups over Integral Domains, Simeon Ivanov (editor), Galois Theory, Rings, Algebraic Groups and Their Applications, American Mathematical Society, page 87, Let R be a Noetherian factorial ring of characteristic p which is not a field.