Equation 677 Database

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Magma dba976f1b126…

magma dba976f1b126
Size
169
Isomorphism class hash
dba976f1b1267cc455f832b2c24df0db38c6e9de3f93160fff3ca0b2db488fb4
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Submitted by
dwrensha
Submitted at
2026-04-28 18:08:12
Display reorder
168,0,129,12,40,26,73,157,101,115,87,54,143,19,14,124,15,107,22,158,86,58,95,126,148,113,80,156,75,119,35,165,76,37,18,59,83,24,2,122,48,125,117,70,102,68,92,39,118,4,161,60,150,98,5,79,145,120,30,153,96,85,67,130,146,136,16,132,106,116,131,62,65,71,53,82,84,139,33,162,109,100,36,29,28,127,140,63,13,121,138,108,6,46,88,147,3,52,103,104,111,25,34,78,61,7,9,166,128,155,149,137,56,41,31,57,91,66,167,55,151,10,21,69,105,45,1,163,142,23,47,135,77,141,43,114,17,152,27,154,42,50,123,164,144,99,8,134,93,112,160,81,110,44,159,72,94,38,64,51,20,133,11,74,97,32,90,49,89 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

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]

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