Find all units of $S$, where $S$ is the set of polynomials in $\mathbb{Q}[x]$ whose coefficient of $x$ is $0$. I think the units are $\mathbb{Q} \setminus \{0\}$. Is that correct?
Polynomials (abstract algebra)
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abstract-algebra
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0What is $Q$? Do you mean the rational numbers, $\mathbb{Q}$? – 2012-04-04
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0Q means the set of rational numbers – 2012-04-04
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0@TheChaz: That was an edit made after Brandon's comment. – 2012-04-04
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0"units of $S$, where $S$ is the set of ..." is a somewhat unusual use of the terminology -- usually in "units *of* $X$", $X$ is a ring; otherwise one would say something like "the units of $\mathbb Q[x]$ that lie in $S$". But it so happens that $S$ is indeed a ring, so you could say "Find all units of $S$, where $S$ is the ring of ...". – 2012-04-04
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0so, what are the units then? – 2012-04-04
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0@max: You're right that the units are $\mathbb Q\setminus \{0\}$ -- but note the direction of the slash; "$/$" has a _different_ meaning in algebra. Now can you start a proof why this is true? We'll help you fill in the gaps where you get into trouble. – 2012-04-04
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0I think I got the proof. Thanks a lot. – 2012-04-04