The following exercise is from Gallian's Contemporary Abstract Algebra:
Show that every nonzero element of ${\bf Z}_n$ is a unit of a zero-divisor.
A unit of a ring is an element which has a multiplicative inverse. A nonzero element $a$ is a commutative ring $R$ is called a zero-divisor if there is a nonzero element in $R$ such that $ab=0$.
Here is my question:
What is a unit of a zero-divisor in this exercise?
Edit:
According to the answers, this is a typo.
Best Answer
It should say "unit OR a zero-divisor". The proof follows immediately from your prior exercise and an application of Bezout's GCD identity to deduce that $\rm\ gcd(m,n)=1\ \Rightarrow\ m\ $ is a unit in $\rm\:\mathbb Z/n\:.$