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Establish, whether or not following subsets of given rings are subrings

  1. All polynomials $f(x)$ with $f(0)=9$ in $\mathbb{Z}[x]$.

These are past paper questions, I have no clue what $\mathbb{Z}[x]$ is, can anyone give me some help please. There are also two more questions:

Establish, whether or not following subsets of given rings are ideals:

  1. All integers divisible by $5$ in $\mathbb{Q}$ ($\mathbb{Q}$ is the field of rational numbers).

  2. All polynomials in $\mathbb{Z}[x]$ with coefficients divisible by $5$ in $\mathbb{Z}[x]$.

Thank you so much

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    $\mathbb Z[X]$ is the ring of polynomials with integer coefficients. If you haven't seen this notation before (or its general form $R[X]$ for an arbitrary ring $R$), are you sure you should be trying to solve that problem set in the first place?2012-04-25

1 Answers 1