Units, zero Divisors?

In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero ... .. Left or right zero divisors can never be units, because if a is invertible and ax = 0, the...

In a finite commutative ring with unity, every element is either a unit or a zero- divisor. Indeed, let a ∈ R and consider the map on R given by x ...

Claim: Let R be a cummatative Ring with 1 ≠ 0. Then holds: i) A zero divisor is never a unit, that implies a Ring with zero divisors is not a field. ii) (R*,·) is a group  ...