MATHEMATICA BOHEMICA, Vol. 137, No. 1, pp. 99-111, 2012

# A generalization of semiflows on monomials

## Hamid Kulosman, Alica Miller

Hamid Kulosman, Department of Mathematics, University of Louisville, Louisville, KY 40292, USA, e-mail: h0kulo01@louisville.edu; Alica Miller, Department of Mathematics, University of Louisville, Louisville, KY 40292, USA, e-mail: a0mill01@louisville.edu

Abstract: 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 $\geq0$.

Keywords: monomial ideal, term ideal, Dickson's lemma, semiflow

Classification (MSC 2010): 37B05, 13A99

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