(adsbygoogle = window.adsbygoogle || []).push({}); Proving that Z2 X Z2 X Z2..... Z2 is a isomorphic (ring isomorphism) to P(N)

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

I wish to prove that the ring of Cartesian product Z2 X Z2 X Z2....X Z2 (here we have n products) under addition and multiplication (Z2 is {0,1}) is isomorphic to P(N) where P(N) is the ring of power set of the set of n elements where the multiplication operation is AB=A U B and the addition operation is A+B=(A U B)-(A[itex]\cap[/itex]B)

2. Relevant equations

Both of these rings are Boolean rings

A ring isomorphism is an operation preserving (both operations) one to one and onto map between the two rings

3. The attempt at a solution

I tried for smaller cases such as Z2 => P(1) and I was able to find an isomorphism through brute force. I want to somehow use the fact that these two rings are Boolean rings to solve this.

While searching for a solution I ran into something called "the Stone Representation theorem" which states that all Boolean Algebras are isomorphic to a field of sets. Is it possible to apply this theorem in this case?

Thank you for the help

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# Homework Help: Proving that Z2 X Z2 X Z2 . Z2 is a isomorphic (ring isomorphism) to P(N)

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