Thread: quotient rings 2

If R is an integral domain and ab=ac for a not equal to 0,b,c in R, show that b=c.

Please show steps. Thanks!

Originally Posted by mpryal

If R is an integral domain and ab=ac for a not equal to 0,b,c in R, show that b=c.

Please show steps. Thanks!

being in an integral domain means you have a commutative ring in which for x and y in the ring, xy = 0 implies x = 0 or y = 0

with that in mind, consider ab - ac = 0