A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 32 semigroups of order six, all of which generate the variety V[7624]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-2e8a57d2c961ca48 in the data of the bases-min seal.
Certified for
[6, 7624] [6, 8188] [6, 8192] [6, 8330] [6, 8380] [6, 8382] [6, 8427] [6, 8429] [6, 8431] [6, 8445] [6, 8458] [6, 10629] [6, 11113] [6, 11242] [6, 11243] [6, 11423] [6, 11432] [6, 11434] [6, 11480] [6, 13214] [6, 13241] [6, 13260] [6, 13442] [6, 13488] [6, 13626] [6, 13632] [6, 13639] [6, 13650] [6, 13651] [6, 13652] [6, 13981] [6, 14163]
The identities
- x² ≈ x³
- x²y ≈ xyx
- xy²z² ≈ xzy²z