(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let R={0, 2, 4, 6, 8} under addition and multiplication modulo 10. Prove that R is a field.

2. Relevant equations

A field is a commutative ring with unity in which every nonzero element is a unit.

3. The attempt at a solution

I know that the unity of R is 6, and that the multiplicative inverse of 2 is 8, of 3 is 2, of 4 is 4, and of 6 is 6.

So I've shown that each nonzero element is a unit.

I'm not sure how to go about showing that R is a commutative ring.

To show the commutative part, I'm guessing that I can just do out the Cayley table of R.

I don't know how to show that R is a ring without going through all of the characteristics of a ring though. I don't think I need to do that but I'm not sure.

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# Homework Help: Abstract Algebra Field Proof

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