Is the set of polynomials $a_0+a_1x+\ldots+a_nx^n$, where $2^{k+1}$ divides $a_k$, an ideal in $\mathbb{Z}[x]$? How should I think about this?
Ideal in $\mathbb{Z}[x]$
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abstract-algebra
ring-theory
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0@martini: nice hint, thanks. – 2012-11-08
1 Answers
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Can you se what happens when you multiply an element of that set by a polynomial; by $x$ for example?
Another approach, your set contains the constant $2$; if it were an ideal, it should contain all polynomials divisible by $2$. Does it?
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0I get it, thanks! – 2012-11-08