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field of fractions for noncommutative rings
Hiya guys, I know that every commutative integral domain has a field of fractions... but I'm just wondering... why does the method of proof not work for noncommutative rings?...
I imagine because, if you follow the proof right to the end and adapt as necessary, your field of fractions will turn out not to be a field, because ab-1 and b-1a are not the same element (so we can't sensibly form a notion of "a/b[noparse]")[/noparse].
If you want any more details, post a sketch of the proof.
If you want any more details, post a sketch of the proof.
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