A certified basis of 5 identities
This list of identities is a basis, proved in Lean, of 21 semigroups of order six, all of which generate the variety V[7428]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-964af2b02d085b5d in the data of the bases-min seal.
Certified for
[6, 7428] [6, 7429] [6, 7497] [6, 7576] [6, 7611] [6, 7820] [6, 7848] [6, 8024] [6, 8052] [6, 10913] [6, 11196] [6, 12576] [6, 12639] [6, 12760] [6, 12794] [6, 12835] [6, 12975] [6, 13007] [6, 13043] [6, 13369] [6, 13936]
The identities
- x² ≈ x³
- x²y² ≈ yxy
- xyx ≈ xyx²
- xyxz ≈ yxyz
- xyzx ≈ xzyx