Can a finite ring have characteristic 0 If so give an exampl

Can a finite ring have characteristic 0? If so, give an example of such a ring, and if not prove that it can\'t.

Solution

No finite ring cannot have characteristic zero.

Consider any finite ring R. Number of elements be n . 0 the additive identity 1 multplicative identity.

Since (R, +, 0) form a group .

a + a + ...... n times = 0 for any a in R

so characteristic of the ring <= n