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Mr Davis 97
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Homework Statement
Consider the quotient ring ##F = \mathbb{Z}_3 [x] / \langle x^2 + 1 \rangle##. Compute the order of the coset ##(x+1) + \langle x^2 + 1 \rangle## in the group of units ##F*##.
Homework Equations
The Attempt at a Solution
I was thinking that I just continually compute powers of (x+1) until I reach a polynomial with ##x^2+1## as a factor, but this is cumbersome. I guess my question, after each computation, how do I reduce the expression to get a simpler description of the coset? Do I just subtract ##x^2 + 1## as many times as a please?
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