Ring Properties of R Defined by Multiples of 4

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The discussion centers on the mathematical structure of the set R, defined as all multiples of 4 within the integers Z. It establishes that (R, +, *) forms a ring with unity, where the unity element is 4. Additionally, the mapping Ø: R → Z, defined by Ø(x) = x/4, is confirmed as an isomorphism, demonstrating a one-to-one correspondence between R and Z under the defined operations.

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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?
 

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