A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 42 semigroups of order six, all of which generate the variety V[7120]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-de132b06ff6548e5 in the data of the bases-min seal.
Certified for
[6, 7120] [6, 7288] [6, 8762] [6, 10055] [6, 10448] [6, 10672] [6, 11752] [6, 11964] [6, 12017] [6, 12043] [6, 12105] [6, 12107] [6, 12140] [6, 12174] [6, 12196] [6, 12227] [6, 12307] [6, 12499] [6, 12510] [6, 12516] [6, 12519] [6, 12524] [6, 13833] [6, 13886] [6, 14023] [6, 14046] [6, 14089] [6, 14189] [6, 14226] [6, 14231] [6, 14329] [6, 14333] [6, 14410] [6, 14415] [6, 14416] [6, 14457] [6, 14461] [6, 14464] [6, 14487] [6, 14506] [6, 14550] [6, 14563]
The identities
- x²y ≈ xy
- xy ≈ xy²
- xy ≈ xyxy
- xyzx ≈ xzyx