Equation 677 Database

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Magma 2925dc18176c…

magma 2925dc18176c
Size
9
Isomorphism class hash
2925dc18176c3a094e546f32ddfbde1b795255106b00f6076737cdc6da05a538
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 8) what is this?
Submitted by
bulk-import-memoryleak47
Submitted at
2026-04-23 20:56:20
Display reorder
8,0,3,4,1,7,2,6,5 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Linear magma over the extension field F_9 = F_3[α]/⟨α² + 1⟩. Operation: x ◇ y = a·x + b·y in F_9 with (a, b) = (1, 2 + α). Note 2 + α is a root of Φ_10(x) = x⁴ - x³ + x² - x + 1 (cyclotomic polynomial for primitive 10th roots of unity) in F_9, and the corresponding α_coef = 1 satisfies α_coef = -β³ - β - 1 - this is Pace Nielsen's "Type 2" linear 677 magma family. F_9 is the proper degree-2 extension of F_3; do NOT confuse with the ring Z/9Z = Z/9 (which has zero divisors and is NOT a field). Size 9, not fully idempotent (only 1 element is idempotent), right-cancellative. [text written by Claude]

last edited by dwrensha at 2026-05-16 12:02:51 · history