Equation 677 Database

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Magma a9267aade1a1…

magma a9267aade1a1
Size
49
Isomorphism class hash
a9267aade1a1ca38e866601f513e4cbf640498155d05f73c82f7db0c3027d5fe
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:58:34
Display reorder
48,0,12,26,41,21,10,45,14,5,39,36,28,24,42,34,32,33,23,35,4,44,20,25,1,29,8,37,47,40,18,6,16,15,17,46,7,11,19,3,22,31,43,27,38,13,9,2,30 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the ring Z/49Z: x ◇ y = 18x + 10y (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. Coefficients (18, 10) satisfy the Eq 677 polynomial conditions over the ring Z/49Z. Size 49, not fully idempotent, right-cancellative. Companion to magma#bd9c4bf0 (also Z/49Z with coefficients (18, 8)). [text written by Claude]

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