Geodesic
A generalization of semiflows on monomials
Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 99-111

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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 $\geq 0$.
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 $\geq 0$.
DOI : 10.21136/MB.2012.142790
Classification : 13A15, 13A99, 13F20, 37B05, 54H20
Keywords: monomial ideal; term ideal; Dickson's lemma; semiflow 
Kulosman, Hamid; Miller, Alica. A generalization of semiflows on monomials. Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 99-111. doi: 10.21136/MB.2012.142790
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[1] Cox, D., Little, J., O'Shea, D.: Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York (2007). | MR | Zbl

[2] Ellis, D., Ellis, R., Nerurkar, M.: The topological dynamics of semigroup actions. Trans. Am. Math. Soc. 353 (2000), 1279-1320. | DOI | MR

[3] Lombardi, H., Perdry, H.: The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics. B. Buchberger, F. Winkler, Gröbner Bases and Applications London Mathematical Society Lecture Notes Series, vol. 151, Cambridge University Press (1988), 393-407. | MR

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