A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 27 semigroups of order six, all of which generate the variety V[1222]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ed4744766dab4ccc in the data of the bases-min seal.
Certified for
[6, 1367] [6, 1398] [6, 3162] [6, 4226] [6, 4230] [6, 4310] [6, 4320] [6, 4322] [6, 7037] [6, 7043] [6, 7052] [6, 8949] [6, 8951] [6, 8957] [6, 8963] [6, 8966] [6, 9027] [6, 9029] [6, 9041] [6, 9043] [6, 9055] [6, 9066] [6, 9068] [6, 9074] [6, 9078] [6, 9082] [6, 9084]
The identities
- x² ≈ x⁴
- xy ≈ yx
- xy ≈ xy³