A certified basis of 6 identities
This list of identities is a basis, proved in Lean, of 111 semigroups of order six, all of which generate the variety V[883]. Removing the identities that follow from the others leaves 3 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-20a9f19583fbe8b0 in the data of the bases-min seal.
Certified for
[6, 883] [6, 884] [6, 885] [6, 888] [6, 889] [6, 891] [6, 892] [6, 893] [6, 894] [6, 895] [6, 896] [6, 897] [6, 899] [6, 900] [6, 901] [6, 903] [6, 904] [6, 906] [6, 907] [6, 913] [6, 916] [6, 920] [6, 921] [6, 922] [6, 931] [6, 933] [6, 936] [6, 937] [6, 939] [6, 940] [6, 941] [6, 942] [6, 943] [6, 944] [6, 945] [6, 946] [6, 947] [6, 949] [6, 950] [6, 951] [6, 953] [6, 954] [6, 956] [6, 957] [6, 2233] [6, 2234] [6, 2235] [6, 2236] [6, 2238] [6, 2239] [6, 2240] [6, 2242] [6, 2243] [6, 2244] [6, 2246] [6, 2248] [6, 2249] [6, 2250] [6, 2251] [6, 2252] [6, 2253] [6, 2254] [6, 2255] [6, 2257] [6, 2261] [6, 2264] [6, 2265] [6, 2267] [6, 2270] [6, 2273] [6, 2274] [6, 2278] [6, 2279] [6, 2280] [6, 2282] [6, 2283] [6, 2284] [6, 2285] [6, 2286] [6, 2288] [6, 2290] [6, 2291] [6, 2292] [6, 2293] [6, 2294] [6, 2295] [6, 2296] [6, 2297] [6, 2299] [6, 2568] [6, 2577] [6, 4833] [6, 4834] [6, 4836] [6, 4837] [6, 4838] [6, 4839] [6, 4841] [6, 4842] [6, 4843] [6, 4846] [6, 4849] [6, 4852] [6, 4853] [6, 4855] [6, 4856] [6, 4857] [6, 4858] [6, 4860] [6, 4861] [6, 4862]
The identities
- x³ ≈ xy²
- x³ ≈ yxy
- x³ ≈ y²x
- xyz ≈ xzy
- xyz ≈ yxz
- x³yz ≈ xyz