Main Page | See live article | Alphabetical index


In abstract algebra, the characteristic of a ring R is defined to be the smallest positive integer n such that 1R+...+1R (with n summands) yields 0. If no such n exists, we say that the characteristic of R is 0.

Alternatively and equivalently, the characteristic of the ring R may be defined as that unique natural number n such that R contains a subring isomorphic to the factor ring Z/nZ.

Examples and notes:

Characteristic is also sometimes used as a piece of jargon in discussions of universals in metaphysics, often in the phrase 'distinguishing characteristics'.