A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 20 semigroups of order six, all of which generate the variety V[9091]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-821427ec4508dd18 in the data of the bases-min seal.
Certified for
[6, 9091] [6, 9092] [6, 9093] [6, 9101] [6, 9102] [6, 9103] [6, 11928] [6, 11932] [6, 14899] [6, 14903] [6, 14908] [6, 14909] [6, 14928] [6, 14931] [6, 14932] [6, 14943] [6, 14947] [6, 14948] [6, 14970] [6, 14975]
The identities
- x² ≈ x⁵
- x⁴y ≈ xy
- x³y² ≈ x²y²x
- xyz ≈ yxz