Field of fractions: Revision history

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27 September 2025

3 December 2024

  • curprev 16:5916:59, 3 December 2024 imported>Semiring&tropical 9,091 bytes +9,091 →Semifield of fractions: The claim that every commutative semiring with no zero divisors has a semifield of fractions is incorrect. When inverting elements of a semiring, the condition needed to have an embedding is that the elements all be multiplicatively cancellative. In the case of rings, not being a zero divisor and being multiplicatively cancellative are equivalent. But for more general semirings, these are not the same. I have included an example in the text.
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