## ZERODIVISOR

### Zero divisor

In abstract algebra, an element of a ring is called a**left zero divisor**if there exists a nonzero such that, or equivalently if the map from to sending to is not injective. Similarly, an element of a ring is called a

**right zero divisor**if there exists a nonzero such that . This is a partial case of divisibility in rings. An element that is a left or a right zero divisor is simply called a

**zero divisor**. An elementÂ that is both a left and a right zero divisor is called a

**two-sided zero divisor**. If the ring is commutative, then the left and right zero divisors are the same.

*The above text is a snippet from Wikipedia: Zero divisor*

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and as such is available under the Creative Commons Attribution/Share-Alike License.