A certified basis of 8 identities
This list of identities is a basis, proved in Lean, of 20 semigroups of order six, all of which generate the variety V[7430]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-ead20961ebd536c9 in the data of the bases-min seal.
Certified for
[6, 7430] [6, 7431] [6, 7498] [6, 7821] [6, 7849] [6, 7977] [6, 7981] [6, 8025] [6, 8053] [6, 8056] [6, 10914] [6, 10918] [6, 12577] [6, 12640] [6, 12795] [6, 13008] [6, 13012] [6, 13044] [6, 13046] [6, 13937]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- xyx ≈ xy²x
- xyx ≈ yxyx
- xyzx ≈ xzyx
- xyxzy ≈ yxzy
- xy²zx ≈ xyzx