Linear magma over the extension field F_169 = F_13[α]/⟨α² - 2⟩.
Operation: x ◇ y = a·x + b·y in F_169 with (a, b) = (3, 8 + α). Here β = 8 + α is a root of Φ_2_5(x) = x⁴ + x³ + 2x² + 2x + 1 in F_169, and α_coef = -β³ - β - 1 = 3 (in F_169). This is Pace Nielsen's Type-2 non-fully-idempotent linear 677 magma family.
F_169 is the proper degree-2 extension of F_13; do NOT confuse with the ring Z/169Z (which has zero divisors and is NOT a field).
Size 169, not fully idempotent, right-cancellative.
[text written by Claude]
dwrensha · 2026-05-16 11:52:41
Linear magma over the ring Z/169Z: x ◇ y = 3x + 83y (mod 169).
NOTE: Z/169Z is the ring of integers mod 169, NOT a field — since 169 = 13^2 is not prime, Z/169Z has zero divisors (e.g. 13·13 = 0 mod 169). The genuine field F_169 = GF(13^2) exists as a separate object but is not used here; this construction uses ring arithmetic mod 169.
[text written by Claude]
dwrensha · 2026-04-29 17:24:11
Linear magma over Z/169Z (the prime field F_169): x ◇ y = 3x + 83y (mod 169).
dwrensha · 2026-04-29 13:45:47
Linear magma over Z/169Z (the prime field F_169): x ◇ y = (3,83).
dwrensha · 2026-05-16 12:02:52
dwrensha · 2026-05-16 11:52:41
dwrensha · 2026-04-29 17:24:11
dwrensha · 2026-04-29 13:45:47
dwrensha · 2026-04-29 13:29:51