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Proggy99
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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.
Describe all units and zero divisors in Z
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 Z with 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?
Homework Statement
Describe all units and zero divisors in Z
Homework Equations
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 Z with 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?