The Characteristic reference article from the English Wikipedia on 24-Jul-2004
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Characteristic

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In mathematics, the characteristic of a ring R with identity element 1R is defined to be the smallest positive integer n such that n1R = 0 (where n1R is defined as 1R + ... + 1R with n summands). If no such n exists, we say that the characteristic of R is 0. The characteristic of R is often denoted char(R).

The characteristic of the ring R may be equivalently defined as the unique natural number n such that nZ is the kernel of the unique ring homomorphism from Z to R which sends 1 to 1R. And yet another equivalent definition: the characteristic of R is the unique natural number n such that R contains a subring isomorphic to the factor ring Z/nZ.

Examples and notes


The term "characteristic" is also used in several other unrelated mathematical contexts:
Characteristic is also sometimes used as a piece of jargon in discussions of universals in metaphysics, often in the phrase 'distinguishing characteristics'.