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Keywords:
monomial ideal; term ideal; Dickson's lemma; semiflow
monomial ideal; term ideal; Dickson's lemma; semiflow
Summary:
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 $\geq 0$.
References:
[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 2290010 | Zbl 1118.13001
[2] Ellis, D., Ellis, R., Nerurkar, M.: The topological dynamics of semigroup actions. Trans. Am. Math. Soc. 353 (2000), 1279-1320. DOI 10.1090/S0002-9947-00-02704-5 | MR 1806740
[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 1708891
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