A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 37 semigroups of order six, all of which generate the variety V[4024]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-43ca512b5c116dfb in the data of the bases-min seal.
Certified for
[6, 4024] [6, 4030] [6, 4033] [6, 4132] [6, 4136] [6, 4139] [6, 4239] [6, 4245] [6, 4248] [6, 6789] [6, 6908] [6, 6935] [6, 7051] [6, 8806] [6, 8812] [6, 8825] [6, 8826] [6, 8832] [6, 8835] [6, 8837] [6, 8892] [6, 8956] [6, 8962] [6, 8975] [6, 8976] [6, 8982] [6, 8985] [6, 8987] [6, 9034] [6, 9881] [6, 10182] [6, 10212] [6, 10363] [6, 10380] [6, 10396] [6, 10403] [6, 11768]
The identities
- x² ≈ x⁴
- x³y ≈ xy
- xyx ≈ yx²
- xyz ≈ yxz