A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 53 semigroups of order six, all of which generate the variety V[15000]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-58c2dddcbbfb8af6 in the data of the bases-min seal.
Certified for
[6, 15000] [6, 15002] [6, 15007] [6, 15014] [6, 15016] [6, 15034] [6, 15037] [6, 15040] [6, 15041] [6, 15066] [6, 15102] [6, 15104] [6, 15109] [6, 15116] [6, 15118] [6, 15199] [6, 15202] [6, 15204] [6, 15205] [6, 15215] [6, 15225] [6, 15253] [6, 15257] [6, 15266] [6, 15267] [6, 15271] [6, 15274] [6, 15276] [6, 15277] [6, 15371] [6, 15380] [6, 15381] [6, 15384] [6, 15390] [6, 15392] [6, 15393] [6, 15482] [6, 15484] [6, 15659] [6, 15661] [6, 15666] [6, 15673] [6, 15675] [6, 15692] [6, 15695] [6, 15698] [6, 15699] [6, 15718] [6, 15750] [6, 15752] [6, 15757] [6, 15764] [6, 15766]
The identities
- x ≈ x²
- xy ≈ yx