Talk:Quasifield
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There seems to be some confusion. Most sources omit the right distributive law (a+b).c=a.c+b.c However some sources omit the other one. Is there a general consensus, or should I make two definitions?
- Just mention there is a choice. I think 'loop' in your sense is probably loop (algebra), which goes to quasigroup. Charles Matthews 19:54, 11 February 2006 (UTC)
Deleted paragraph
[edit]I deleted the following paragraph, because I think it detracts somewhat from the main points:
"If it is not a division ring, the plane is never desarguesian. However, as the order of a quasifield is always a prime power, one cannot expect to find counterexamples for the conjecture that the order of a projective plane is always a prime power."
The fact that a plane is desarguesian iff its associated planary ternary ring is a division ring is better discussed in projective plane; if someone wants to emphasize it, it would make more sense to do so in planar ternary ring than here. And I'm not sure what the "However" is supposed to entail in the next sentence. Also, I agree that the prime power order problem is somewhat underplayed in projective plane (it is buried in the Properties section), but I'm not sure if it really has the status of a conjecture. All that being said, if someone is really attached to the paragraph, feel free to restore it, but please consider rewording it. --Michael Kinyon 17:30, 1 August 2006 (UTC)
Definition of semifield correct?
[edit]As far as I know in a semifield the additive group is merely a semigroup. But in the definition in this article a semifield would require the addition to be a group.