Talk:Hyperstructure

Expansion request

It would be nice if this article defined a hypergroup. Currently a good reference can be found on planetmath - hypergroup and also a hyperfield which, from what I can tell is the hyper analog of a field. Bonus points - provide examples, such as the Krasner hyperfield $K=\{0,1\}$ and the hyperfield of signs $S=\{-1,0,1\}$ and some example extensions.

My understanding is that the classification of the finite extensions of the Krasner field is unknown (is an open question). Exactly why this is a hard question and how this abuts onto projective geometry would also be a nice paragraph or two.

Then there is stuff to be said about hyperrings and their spectra. That is, both the Krasner hyperfield and the hyperfield of signs are hyper-rings, what is $Spec(K)$ and $Spec(S)$? 67.198.37.16 (talk) 17:10, 26 May 2021 (UTC)