(adsbygoogle = window.adsbygoogle || []).push({}); Rings and Fields - Write down the nine elements of F9

1. The problem statement, all variables and given/known data

In F9 = Z/3Z, there is no solution of the equation x^2 = −1, just as in R. So “invent”

a solution, call it 'i'. Then 'i' is a new “number” which satisfies i^2 = −1. Consider

the set F9consisting of all numbers a+bi, with a,b in F9. Add and multiply these

numbers as though they were polynomials in 'i', except whenever you get i^2 replace

it by −1.

(i) Write down the nine elements of F9.

(ii) Show that every nonzero element of F9has an inverse, so that F9is a

field.

3. The attempt at a solution

I know im supposed to show you that ive tried the question if i want an answer. Believe me, i have tried it. Im just really confused by the wording of the question and am not really sure what they are looking for in part a. Once i get part a, im pretty sure id be able to get part b on my own.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Rings and Fields - Write down the nine elements of F9

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