Equation 677 Database

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Magma bd9c4bf04842…

magma bd9c4bf04842
Size
49
Isomorphism class hash
bd9c4bf04842e2985c41b595e9243858f92359259c97b118f4c0aa0eb8ec7ca0
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:32
Display reorder
48,34,33,9,24,20,1,42,39,29,11,22,17,0,43,41,32,13,27,14,2,47,38,28,8,25,18,3,44,37,31,10,23,15,4,45,36,40,12,21,19,5,46,35,30,7,26,16,6 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

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]

last edited by dwrensha at 2026-05-16 12:02:52 · history