Size-89 non-right-cancellative Eq677 magma with right identity e.
Carrier: {e} ∪ (Z/11Z × Z/8Z). Each set {e} ∪ ({i} × Z/8Z) is a copy of F_9, with e identified with 0 and operation u ◇ v = u + βv, where F_9 = F_3[α]/(α² + 1) and β = 2 + α.
For distinct base labels i,j, define (i,s) ◇ (j,t) = (6i + 6j, t) if j−i ∈ {1,3,4,5,9} mod 11, and (6i + 6j, −s−t) otherwise; first coordinates are mod 11 and second coordinates mod 8.
The rows are permutations, but columns are not: in the supplied table labeling, 1 ◇ 9 = 2 ◇ 9 = 49. Thus this is a right-unital left quasigroup that is not a quasigroup. The magma is nonmedial and satisfies E255. Exhaustive replay checks all 7,921 E677 instances and all 89 E255 instances.
omegaestable · 2026-09-30 18:21:35