Is Not a Zero Divisor?

An element of a ring that is left and right cancellable, and is hence not a zero divisor, is called regular or cancellable, or a non-zero-divisor. A zero divisor that is nonzero is called a nonzero zero divisor or a nontrivial zero divisor.

What do you mean by zero divisor give an example?

In a ring , a nonzero element is said to be a zero divisor if there exists a nonzero such that . For example, in the ring of integers taken modulo 6, 2 is a zero divisor because . However, 5 is not a zero divisor mod 6 because the only solution to the equation is . 1 is not a zero divisor in any ring.

Can a zero divisor be a unit in a ring?

(a) A field is a commutative ring F with identity 1 , 0 in which every nonzero element is a unit, i.e., U(F) = F \{0}. (b) Zero divisors can never be units. ... A commutative ring with identity 1 , 0 is called an integral domain if it has no zero divisors.