Monomial ideal
= Monomial ideal
{wiki}
An <ideal> in a <polynomial ring> generated by <monomials>. Its exponent vectors form an upward-closed subset of $\mathbb N^r$ under the componentwise order. The <Dickson lemma> makes the minimal exponent set finite. This description permits <Maclagan's theorem> to compare ideals by reverse inclusion independently of the coefficient field.