(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove that the ring R of polynomials with real coefficients (i.e. f(x) = a_{0}+ a_{1}x + ... + a_{n}x^{n}, a_{i}real, are elements of R) has only the constant term a_{0}as the group of units, providing the constant term isn't zero.

2. Relevant equations

u is a unit if there exists a v such that uv=1

3. The attempt at a solution

Clearly all the constant terms are units of the ring as we are dealing with the real numbers.

Claim: There are more than just these, and that a polynomial f(x) = a_{0}+ a_{1}x + ... + a_{n}x^{n}is invertible.

=> there must exist a g(x) = b_{0}+ b_{1}x + ... + b_{n}x^{n}

such that f(x).g(x) = 1

f(x).g(x) = b_{0}(a_{0}+ a_{1}x + ...) + b_{1}x(a_{0}+ a_{1}x + ...) + b_{2}x^{2}(a_{0}+ a_{1}x + ...) + ... = 1

Not too sure where to go from here.. Sorry if my notation is a little off but hopefully you can understand

Thanks

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Finding the units (number theory)

**Physics Forums | Science Articles, Homework Help, Discussion**