A certified basis of 16 identities
This list of identities is a basis, proved in Lean, of 63 semigroups of order six, all of which generate the variety V[3541]. Removing the identities that follow from the others leaves 7 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-b99d0a62e56fe4fc in the data of the bases-min seal.
Certified for
[6, 3541] [6, 3543] [6, 3551] [6, 3739] [6, 3740] [6, 3743] [6, 3792] [6, 3794] [6, 3795] [6, 3798] [6, 3844] [6, 3858] [6, 3863] [6, 3865] [6, 3928] [6, 6468] [6, 6469] [6, 6470] [6, 6547] [6, 7578] [6, 7579] [6, 7580] [6, 7613] [6, 8161] [6, 8164] [6, 8167] [6, 8170] [6, 8171] [6, 8179] [6, 8181] [6, 8183] [6, 8255] [6, 8262] [6, 8263] [6, 8266] [6, 8267] [6, 8311] [6, 8312] [6, 8322] [6, 8370] [6, 8375] [6, 8407] [6, 8414] [6, 8419] [6, 8480] [6, 8485] [6, 8679] [6, 10788] [6, 10910] [6, 11198] [6, 11199] [6, 11200] [6, 11201] [6, 11221] [6, 11499] [6, 13206] [6, 13236] [6, 13252] [6, 13296] [6, 13374] [6, 13375] [6, 13609] [6, 13973]
The identities
- x² ≈ x³
- x²yx ≈ xyx
- xyx ≈ xyx²
- x²y² ≈ xyxy
- xyxy ≈ xy²x
- xyxy ≈ yx²y
- xyxzx ≈ xyzx
- x²yzy ≈ xyxzy
- xyxzy ≈ yx²zy
- xyxz² ≈ xyzxz
- xyzxy ≈ xyzyx
- xyzxy ≈ yxzxy
- xyzxz ≈ xyz²x
- xyxztz ≈ xyzxtz
- xyzxty ≈ yxzxty
- xyztxz ≈ xyztzx