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Show that the set of all polynomials $f(x)$ of degree at most $5$ with integer coefficients is a ring. Is the set of such polynomials a field?

I don't see how the ring of polynomials with degree at most $5$ is closed under multiplication. If I multiply $x^2$ and $x^5$ I do not get another polynomial of degree at most $5$.

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    Well, they are not a ring, so it is not surprising that you cannot see it!2011-04-01
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    $\:\mathbb Z\:$ is the only subring of $\rm\:\mathbb Z[x]\:$ of bounded degree. Check the question.2011-04-01

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