# Answer to Question #16531 in Abstract Algebra for Hym@n B@ss

Question #16531

Show that the characteristic of a domain is either 0 or a prime number

Expert's answer

Suppose the domain

prime, then

(

*R*has characteristic*n<>*0. If*n*is not aprime, then

*n*=*n*1*n*2 where 1*< ni < n*. But then*ni*1*<>*0, and(

*n*1*1)(*n*2*1) =*n*1 = 0 contradicts the fact that*R*is a domain
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