Im soooooo close to solving this problem (Rings)

[pureouchies4717]

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

 

[Data]

You know m 1_R=0_R. You need to show that there are some x, y in R with x\cdot (n 1_R) = 0_R and (n 1_R) \cdot y = 0_R.

I suggest trying y=x = \frac{m}{(n,m)}1_R.