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# Def/Zero divisor

Definition of Zero divisor: Suppose that $R$ is a commutative ring. A zero divisor (in $R$) is a nonzero element $x \in R$, such that $\exists y \in$R$satisfying the following two conditions: •$xy = 0$. •$y \neq 0\$.

## Logical Connections

This definition logically relies on the following definitions and statements: Def/Commutative, Def/Ring

The following statements and definitions logically rely on the material of this page: Def/Integral domain, and State/Root counting over a field

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