A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 46 semigroups of order six, all of which generate the variety V[7673]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-1a6e5477908acf05 in the data of the bases-min seal.
Certified for
[6, 7673] [6, 7677] [6, 8230] [6, 8235] [6, 8498] [6, 8501] [6, 8502] [6, 8505] [6, 10423] [6, 10427] [6, 10639] [6, 10641] [6, 10986] [6, 10991] [6, 11121] [6, 11123] [6, 11272] [6, 11549] [6, 11553] [6, 13554] [6, 13556] [6, 13557] [6, 13564] [6, 13566] [6, 13568] [6, 13569] [6, 13570] [6, 13574] [6, 13575] [6, 13576] [6, 13748] [6, 13749] [6, 13751] [6, 13757] [6, 13758] [6, 13761] [6, 13762] [6, 13763] [6, 13764] [6, 13769] [6, 13770] [6, 13771] [6, 13772] [6, 14002] [6, 14004] [6, 14378]
The identities
- x² ≈ x³
- xy ≈ xy²
- x²y ≈ x²yx
- xyxz ≈ xyxzx