This is my first assignment in my Modern (Abstract) Algebra class, just to give an idea where I am with tools that I can use.(adsbygoogle = window.adsbygoogle || []).push({});

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

Describe all units and zero divisors in Z

2. Relevant equations

3. The attempt at a solution

I already know the answers are units = 1, -1, i, -i

and zero divisors: none

I know I can get 1 and -1 by setting them up as multiplicative inverses:

1x = 1(mod i) and -1x = 1(mod i) where x is 1 and i-1 respectively.

But I am not sure how to go about getting i and -i, nor do I agree with them based on my understanding and previously worked problems. One question I have is why the book writes Zwith brackets when it never uses brackets when the mod is an actual number or when it is the variable n. Am I missing something special with that notation?

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# Modern Algebra - units and zero divisors

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