Ring Properties of R Defined by Multiples of 4

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1. Consider the set Z of integers, and let R denote the subset all multiples of 4. Define addition as ordinary addition in Z, and define multiplication * in R by a*b = ab/4

a. Show that (R, +, *) is a ring with unity (what is the unity of R?)

b. Show that the mapping Ø: R → Z defined by Ø(x) = x/4 is an isomorphism
 
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That looks straightforward enough. Why don't you just prove those things? What's stopping you?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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