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Reduced ring

An element of a ring is called nilpotent if there exists some positive integer n such that .

A ring R is said to be reduced if it has no non-zero nilpotent elements.

Since every zero divisor in is nilpotent, the nilpotent condition is weaker than having no zero divisors. Consequently,  every domain is a reduced ring, but not every reduced ring is a domain..

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