Im soooooo close to solving this problem (Rings)

[pureouchies4717]

Question: Let R be a ring of characteristic m > 0, and let n be any
integer. Show that if 1 < gcd(n,m) < m, then n · 1R is a zero divisor



heres what i got out of this:

Let gcd(n,m) = b

1< d < m so m/d = b < m
and d | n


Also, m * 1_R = 0

can someone please offer some insight?
thanks,
nick

 

[StatusX]

I don't follow you at all. What is d?

If a ring has characteristic m, then the elements n*1_R which are zero are exactly those with n a multiple of m. So to show n is a zero divisor, you need to find another integer k such that nk is a multiple of m, but k is not, ie, n*1_R k*1_R=0, but k*1_R is not 0.