Take the 2-minute tour ×  The following is an exercise in
Hungerford (Ch. III, ex. 5.6).  Let $R$ be a commutative ring
with identity. If $f=a_nx^n+\dots+a_0$ is a zero divisor in
$R[x]$, then there exists a nonzero $b$ in $R$ such that
$ba_n=ba_{n-1}=\dots=ba_0=0$.  I can see for example that
$\{g\in R[x]\mid fg=0\}$ is a nonzero ideal, so it contains a
nonzero element of smallest degree. But how to show that such an
element is actually a constant?  share|improve this question
Thanks rschwieb. The question in the other post is not an exact
duplicate, but the answer from Gone proves the general case. – 
PatrickR Dec 21 '12 at 21:24 If you want you can delete it, but
in this case you don't have to do anything. If someone really
doesn't like it, they'll have to vote to delete. Please don't
edit the other question's contents. –  rschwieb Dec 21 '12 at
21:24 I've made a meta question on the issue of near duplicates:
meta.math.stackexchange.com/questions/6941/… –  Hurkyl Dec 21
'12 at 21:34 I gave here a complete