A certified basis of 2 identities
This list of identities is a basis, proved in Lean, of 35 semigroups of order six, all of which generate the variety V[5612]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-02fe3dfe4685a6a2 in the data of the bases-min seal.
Certified for
[6, 5612] [6, 5620] [6, 5630] [6, 5632] [6, 5634] [6, 5643] [6, 5649] [6, 5653] [6, 9439] [6, 9443] [6, 9449] [6, 9455] [6, 9457] [6, 9581] [6, 9585] [6, 9586] [6, 9588] [6, 9593] [6, 9707] [6, 9710] [6, 9716] [6, 9717] [6, 9718] [6, 9720] [6, 9721] [6, 9723] [6, 9724] [6, 9725] [6, 9735] [6, 9737] [6, 9738] [6, 9744] [6, 9757] [6, 9771] [6, 9779]
The identities
- x³ ≈ x⁴
- x²y ≈ xyx