U(Z[x]) ?by 1800bigk Tags: None 

#1
Oct2505, 01:20 PM

P: 42

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? or do I have to find the multiplicative identity? I was thinking about both cases and the number of polynomials with a multiplicative inverse is pretty limited, isn't it? f(x)=1 or f(x)=1. 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.




#2
Oct2505, 04:17 PM

Emeritus
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PF Gold
P: 16,101





#3
Oct2505, 04:41 PM

P: 42

am I right about f(x)=1 and f(x)= 1 being the only polynomial in U(Z[x]) or is there more? would contradiction be the best way, how would I start it?
tia 



#4
Oct2505, 04:46 PM

Emeritus
Sci Advisor
PF Gold
P: 16,101

U(Z[x]) ?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. 



#5
Oct2505, 04:51 PM

P: 42

ok thanks!



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