- #1

cooljosh2k2

- 69

- 0

**Rings and Fields - Write down the nine elements of F9**

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 F9

## Homework Statement

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 F9

*consisting 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 F9numbers 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 F9(ii) Show that every nonzero element of F9

*has an inverse, so that F9**is a*

field.

I know I am supposed to show you that I've tried the question if i want an answer. Believe me, i have tried it. I am 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, I am pretty sure id be able to get part b on my own.

field.

## The Attempt at a Solution

I know I am supposed to show you that I've tried the question if i want an answer. Believe me, i have tried it. I am 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, I am pretty sure id be able to get part b on my own.