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monomial ideal; term ideal; Dickson's lemma; semiflow
Let $K$ be a field, $A=K[X_1,\dots , X_n]$ and $\mathbb {M}$ the set of monomials of $A$. It is well known that the set of monomial ideals of $A$ is in a bijective correspondence with the set of all subsemiflows of the $\mathbb {M}$-semiflow $\mathbb {M}$. We generalize this to the case of term ideals of $A=R[X_1,\dots , X_n]$, where $R$ is a commutative Noetherian ring. A term ideal of $A$ is an ideal of $A$ generated by a family of terms $cX_1^{\mu _1}\dots X_n^{\mu _n}$, where $c\in R$ and $\mu _1,\dots , \mu _n$ are integers $\geq 0$.
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