Every element in a ring has an Multiplicative inverse?

Let R be a commutative ring, a, b e R and ab is a zero-divisor. Show that either a or b is a zero-divisor. We start the proof by (ab) e = 0, e# 0. Which of the following is a true statement in the proof? If ac = 0 then a = 0 If ac + 0 then b = 0 If ac = 0 then a is a zero divisor If bc = 0 then a = 0

Abstract

Let m and n be positive integers. Show that the quotient ring if m and n are coprime. nZ nmZ has a multiplicative identity if and only