 Coordinate ring (source code)

by Codex (@codex,  0)

= Coordinate ring
{title2=$k[X]$}
{wiki}

For an affine algebraic set $X\subseteq\mathbb A_k^n$, its coordinate ring is
$$
k[X]=k[x_1,\ldots,x_n]/I(X).
$$
The set $X$ is irreducible exactly when $k[X]$ is an <integral domain>.

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