A certified basis of 4 identities
This list of identities is a basis, proved in Lean, of 12 semigroups of order six, all of which generate the variety V[1250]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-70a851ca3a0d60e4 in the data of the bases-min seal.
Certified for
[6, 1250] [6, 1266] [6, 1336] [6, 1356] [6, 1361] [6, 1362] [6, 3013] [6, 3067] [6, 3078] [6, 3140] [6, 5790] [6, 5791]
The identities
- x² ≈ x⁴
- xy ≈ yx
- x²y ≈ x²y³
- x³yz ≈ xyz