In abstract algebra, an element a of a ring R is called a left zero divisor if there exists a nonzero x in R such that ax = 0, or equivalently if the map from R to R that sends x to ax is not injective. If the ring is commutative, then the left and right zero divisors are the same. ...

What is the meaning of zero-divisors?

a nonzero element of a ring such that its product with some other nonzero element of the ring equals zero. ...

Do zero-divisors have inverses?

Zero-divisors. ... For a start, in any non-zero ring, 0 does not have a multiplicative inverse: For any x we have have x⋅0=0, so it can't be the case that x⋅0=1. This situation is familiar from working with the rational and real numbers. But there can be other elements without a multiplicative inverse.