Linear magma over the ring Z/49Z: x ◇ y = 18x + 8y (mod 49).
NOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7² is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7²) exists as a separate object (and gives different size-49 Eq 677 magmas, e.g. magma#3d9ea61f); this construction uses ring arithmetic mod 49 instead. Bernhard Reinke flagged this distinction.
Coefficients (18, 8) satisfy the Eq 677 polynomial conditions over the RING Z/49Z (verified: 8·(18 + 8·18·8) = 1 and 18 + 8³ + 8²·18² = 0 mod 49).
Size 49, not fully idempotent, right-cancellative.
[text written by Claude]
dwrensha · 2026-05-16 11:52:40
Linear magma over the ring Z/49Z: x ◇ y = 18x + 8y (mod 49).
NOTE: Z/49Z is the ring of integers mod 49, NOT a field — since 49 = 7^2 is not prime, Z/49Z has zero divisors (e.g. 7·7 = 0 mod 49). The genuine field F_49 = GF(7^2) exists as a separate object but is not used here; this construction uses ring arithmetic mod 49.
[text written by Claude]
dwrensha · 2026-04-29 17:22:47
Linear magma over Z/49Z (the prime field F_49): x ◇ y = 18x + 8y (mod 49).
dwrensha · 2026-04-29 17:19:24
Linear magma over Z/49Z (the prime field F_49): x ◇ y = 18x + 8y (mod 49).
dwrensha · 2026-04-29 13:44:00
Linear magma over Z/49Z (the prime field F_49): x ◇ y = (18,8).
dwrensha · 2026-05-16 12:02:52
dwrensha · 2026-05-16 11:52:40
dwrensha · 2026-04-29 17:22:47
dwrensha · 2026-04-29 17:19:24
dwrensha · 2026-04-29 13:44:00
dwrensha · 2026-04-29 13:28:37