### A generalization of semiflows on monomials

Let $K$ be a field, $A=K[{X}_{1},\cdots ,{X}_{n}]$ 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 $A=R[{X}_{1},\cdots ,{X}_{n}]$, where $R$ is a commutative Noetherian ring. A term ideal of $A$ is an ideal of $A$ generated by a family of terms $c{X}_{1}^{{\mu}_{1}}\cdots {X}_{n}^{{\mu}_{n}}$, where $c\in R$ and ${\mu}_{1},\cdots ,{\mu}_{n}$ are integers $\ge 0$.