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  "body": "\n## Definition\n\nLet $A$ be an algebra whose universe is a nonempty [[finite set|070R982G4B]].\nThe algebra $A$ is *quasi-primal* if the [[ternary discriminator|72PG6XCQ7D]] $t$ on $A$ is a [[term operation|N9M2N27END]] of $A$.\nHere $t(x, y, z) = z$ if $x = y$, and $t(x, y, z) = x$ if $x \\ne y$.\n\n## Remarks\n\nExample: every finite field $F$ with $q$ elements, as a ring, is quasi-primal.\nCheck: the term $x + (z - x)\\bigl(1 - (x - y)^{q - 1}\\bigr)$ gives $z$ when $x = y$, and gives $x$ otherwise since then $(x - y)^{q - 1} = 1$.\nNon-example: the two-element lattice $(\\set{0, 1}, \\wedge, \\vee)$ is not quasi-primal.\nIts term operations are monotone, but the discriminator is not, since $t(0, 0, 1) = 1$ while $t(0, 1, 1) = 0$.\nA finite algebra is quasi-primal if and only if it generates an arithmetical variety and every nontrivial subalgebra of it is simple.\nThis characterization is due to Alden Pixley.\n",
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