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  "body": "\n## Definition\n\nLet $A$ be an algebra whose universe is a [[finite set|070R982G4B]] with at least two elements.\nThe algebra $A$ is *primal* if every operation $f \\colon A^n \\to A$ with $n \\ge 1$ is a [[term operation|N9M2N27END]] of $A$.\nEquivalently, the set of basic operations of $A$ is [[functionally complete|TDZVCWYJ9F]].\n\n## Remarks\n\nExample: the ring $(\\Z_p, +, \\cdot, -, 0, 1)$ for a prime $p$ is primal.\nCheck: the polynomial $\\delta(x) = 1 - x^{p - 1}$ equals $1$ at $0$ and $0$ elsewhere, by Fermat's little theorem.\nThen $f(a_1, \\dots, a_n) = \\sum_{b \\in \\Z_p^n} f(b) \\prod_{i} \\delta(a_i - b_i)$, and each $f(b)$ is a sum of copies of $1$.\nNon-example: the field $\\F_4$ with its ring operations is not primal.\nIts Frobenius map $x \\mapsto x^2$ is an automorphism, and term operations commute with automorphisms.\nA constant operation with value outside $\\F_2$ does not commute with it, so it is not a term operation.\nEvery primal algebra is [[quasi-primal|QWSBDFM47K]].\n",
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