Prove that A Ring (R,+,.) has no zero divisor if and only if cancellation law holds in R.

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Proving that a ring R has no zero divisors if and only if the cancellation laws hold in R Proving that a ring R has no zero divisors if and only if the cancellation laws hold in R
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Theorem: the cancellation laws hold in a ring R if and only if R has no zero divisors Theorem: the cancellation laws hold in a ring R if and only if R has no zero divisors
theorem: ring R has no zero divisors iff cancellationlaws hold ,division ring has no zero divisors theorem: ring R has no zero divisors iff cancellationlaws hold ,division ring has no zero divisors