Question

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

Answer 1

Suppose the domain R has characteristic n<> 0. If n is not a
prime, then n = n1n2 where 1 < ni < n. But then ni1 <> 0, and
(n1*1)(n2*1) = n1 = 0 contradicts the fact that R is a domain