Just a pregrad-level curiosity:(adsbygoogle = window.adsbygoogle || []).push({});

I see often repeated (in the Wikipedia page defining "Field", for one) that, from the field's axioms, it can be deduced that F,+ and F\{0},* are both commutative groups.

Yet, the closure property of * is only guaranteed on F, not necessarily on F\{0}. If I'm not mistaken, the finite field Z/6Z is a counter-example: 2*3=0 (mod 6), so {1,2,3,4,5} cannot be a group under multiplication. Is that correct?

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# Abelian groups from the definition of a field

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