Geodesic
A generalization of semiflows on monomials
Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 99-111
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{10_21136_MB_2012_142790,
     author = {Kulosman, Hamid and Miller, Alica},
     title = {A generalization of semiflows on monomials},
     journal = {Mathematica Bohemica},
     pages = {99--111},
     year = {2012},
     volume = {137},
     number = {1},
     doi = {10.21136/MB.2012.142790},
     mrnumber = {2978448},
     zbl = {1249.37001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142790/}
}
TY  - JOUR
AU  - Kulosman, Hamid
AU  - Miller, Alica
TI  - A generalization of semiflows on monomials
JO  - Mathematica Bohemica
PY  - 2012
SP  - 99
EP  - 111
VL  - 137
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142790/
DO  - 10.21136/MB.2012.142790
LA  - en
ID  - 10_21136_MB_2012_142790
ER  - 
%0 Journal Article
%A Kulosman, Hamid
%A Miller, Alica
%T A generalization of semiflows on monomials
%J Mathematica Bohemica
%D 2012
%P 99-111
%V 137
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2012.142790/
%R 10.21136/MB.2012.142790
%G en
%F 10_21136_MB_2012_142790
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

[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

Cité par Sources :