A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 29 semigroups of order six, all of which generate the variety V[993]. Removing the identities that follow from the others leaves 4 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-983d33d229294ee3 in the data of the bases-min seal.
Certified for
[6, 993] [6, 994] [6, 995] [6, 996] [6, 997] [6, 998] [6, 999] [6, 1007] [6, 1008] [6, 1009] [6, 1064] [6, 1065] [6, 1066] [6, 1067] [6, 2959] [6, 2961] [6, 3360] [6, 3361] [6, 3365] [6, 3366] [6, 3369] [6, 3375] [6, 3970] [6, 3971] [6, 5913] [6, 5914] [6, 6153] [6, 6154] [6, 6158]
The identities
- x² ≈ x³
- xyx ≈ xy²
- xyx ≈ yx²
- x²yz ≈ xyz