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I'm trying to do Exercise 1.6.13 (2) in Page 18 of these lecture notes: http://home.math.au.dk/holger/eca05.pdf

The question here asks to determine the units in $\mathbb{Z}[X]/(1-2X)$. I'm not really sure how to start on this. What is the best way to go about this and such problems?

PS I'm aware there is another question with this title but this question is slightly different because the polynomial here isn't monic so the division algorithm isn't available.

user26857
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Anamaki
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    $2X\equiv 1$ in this ring. Do you know another ring $\Bbb Z$ sits inside of with an element that behaves like $X$ does here? – Stahl Mar 13 '17 at 07:09

1 Answers1

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Consider the ring homomorphism $\varphi\colon\mathbb{Z}[X]\to\mathbb{Q}$ defined by $\varphi(f)=f(1/2)$.

What's the kernel of $\varphi$? What's its image?

egreg
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