A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 24 semigroups of order six, all of which generate the variety V[1051]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-13417fe15d589e0f in the data of the bases-min seal.
Certified for
[6, 1051] [6, 1128] [6, 1138] [6, 1211] [6, 1217] [6, 1221] [6, 2926] [6, 2974] [6, 3010] [6, 3015] [6, 3019] [6, 3060] [6, 3618] [6, 3620] [6, 3984] [6, 4003] [6, 4009] [6, 5787] [6, 5796] [6, 6156] [6, 6159] [6, 6162] [6, 6623] [6, 9816]
The identities
- x² ≈ x³
- xy ≈ yx
- x²y ≈ xy²
- x²yz ≈ xyz