A certified basis of 3 identities
This list of identities is a basis, proved in Lean, of 71 semigroups of order six, all of which generate the variety V[7538]. Removing the identities that follow from the others leaves 2 identities (Vampire); the variety page shows the shortest known basis.
Identifier sb-53033be0ecb65b38 in the data of the bases-min seal.
Certified for
[6, 7538] [6, 7545] [6, 7678] [6, 8286] [6, 8291] [6, 8508] [6, 8626] [6, 8682] [6, 8785] [6, 8786] [6, 10001] [6, 10119] [6, 10412] [6, 10414] [6, 10421] [6, 10634] [6, 10637] [6, 10645] [6, 10663] [6, 10671] [6, 11156] [6, 11160] [6, 11161] [6, 11168] [6, 11169] [6, 11274] [6, 11601] [6, 11642] [6, 11658] [6, 11683] [6, 13161] [6, 13164] [6, 13165] [6, 13166] [6, 13167] [6, 13170] [6, 13192] [6, 13193] [6, 13194] [6, 13195] [6, 13199] [6, 13577] [6, 13578] [6, 13579] [6, 13585] [6, 13586] [6, 13587] [6, 13588] [6, 13773] [6, 13774] [6, 13775] [6, 13776] [6, 13963] [6, 13966] [6, 13967] [6, 14005] [6, 14006] [6, 14157] [6, 14158] [6, 14159] [6, 14269] [6, 14338] [6, 14341] [6, 14342] [6, 14509] [6, 14510] [6, 14511] [6, 14512] [6, 14513] [6, 14536] [6, 14538]
The identities
- x² ≈ x³
- xy ≈ xyx
- x²yz ≈ x²zy