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Title: A generalization of semiflows on monomials (English)
Author: Kulosman, Hamid
Author: Miller, Alica
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959
Volume: 137
Issue: 1
Year: 2012
Pages: 99-111
Summary lang: English
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Category: math
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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 $\geq 0$. (English)
Keyword: monomial ideal
Keyword: term ideal
Keyword: Dickson's lemma
Keyword: semiflow
MSC: 13A99
MSC: 37B05
idZBL: Zbl 1249.37001
idMR: MR2978448
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Date available: 2012-04-19T00:04:03Z
Last updated: 2013-09-22
Stable URL: http://hdl.handle.net/10338.dmlcz/142790
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Reference: [1] Cox, D., Little, J., O'Shea, D.: Varieties and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra.Springer, New York (2007). Zbl 1118.13001, MR 2290010
Reference: [2] Ellis, D., Ellis, R., Nerurkar, M.: The topological dynamics of semigroup actions.Trans. Am. Math. Soc. 353 (2000), 1279-1320. MR 1806740, 10.1090/S0002-9947-00-02704-5
Reference: [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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