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Let $R[x]$ be a polynomial ring. Show that if $R$ is finite and has zero divisors, $R[x]$ has an infinite number of zero divisors.

I'm having trouble wrapping my head around what exactly polynomial rings are. And hints pointing me in the right direction would be appreciated.

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    @Carly Any zero divisors in $R$ could be zero divisors in $R[X]$, understood as constant polynomials, among others.2012-11-17

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If $r$ is an element of $R$ such that $r$ is a zero divisor, then $r$ is an element of $R[x]$, and $rx, rx^2, ..., rx^n,...$ are all elements of $R[x]$, and since $\Bbb N$ is infinite, there is an infinite number of zero divisors.

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    Here by zero divisor you mean that $\exists s\ne 0$ s.t. $sr=0$ right? Because $rs=0$ wouldn't work2018-02-25