14 lines
499 B
TeX
14 lines
499 B
TeX
\section{Definition and Examples}
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\begin{definition}[Zero Divisors]
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A \textit{zero-divisor} is a nonzero element $a$ of a commutative ring $R$ such that there is a nonzero element $b \in R$ with $ab = 0$.
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\end{definition}
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\begin{definition}[Integral Domain]
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An \textit{integral domain} is a commutative ring with unity and no zero-divisors.
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\end{definition}
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\begin{theorem}[Cancellation]
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Let $a,b$, and $c$ belong to an integral domain If $a \neq 0$ and $ab = ac$, then $b = c$.
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\end{theorem}
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