Let R be a ring with unity
Prove that if x in R is a unit in R, then x is not a zero-divisor in R.
Show an example of a ring, R, and an element x in R, such that x is not zero, x is not a unit and x is not a zero-divisor of R.
Let R be a ring with unity
Prove that if x in R is a unit in R, then x is not a zero-divisor in R.
Show an example of a ring, R, and an element x in R, such that x is not zero, x is not a unit and x is not a zero-divisor of R.