From An Introduction to Abstract Algebra by T. Hungerford
Section 3.2 #29
Let R be a ring with identity and no zero divisors.
If ab is a unit in R prove that a and b are units.
c is a unit in R if and only if there exists an element x in R s.t. cx=xc=1
where 1 is the identity element of R.
c is a zero divisor in R if and only if 1)c is not equal to 0 and 2)there exists
and element d in R s.t. either cd=0 or dc=0.
The Attempt at a Solution
Any help please? Thank you.