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- Thread starter 1800bigk
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Hurkyl

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It means to find all elements of Z[x] with a multiplicative inverse. (That's what it means to be a unit)Hi, I have to find the units of Z[x]. I am little unclear and my book does not go into detail. Does U(Z[x]) mean I need to find every polynomial with integer cooefficients that has a multiplicative inverse?

That sounds plausible... can you work it into a rigorous proof?As for inverses of polynomials, there would be none because if you multiply a polynomial with x by another polynomial with x then the powers of x get bigger.

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tia

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Hurkyl

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I generally hate answering this question. Learning how and when to be confident in your own work is important! But yes, you are correct.am I right about f(x)=1 and f(x)= -1 being the only polynomial in U(Z[x])

There are lots of ways. I would suggest starting with a literal translation of what you said:would contradiction be the best way, how would I start it?

If p(x) and q(x) are nonconstant, then p(x)*q(x) is nonconstant.

(Actually, you made a stronger statement, but I don't want to spoil figuring out how to translate that!)

And see if you can prove this statement and relate it to inverses.

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ok thanks!

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