| Title:
|
A generalization of semiflows on monomials (English) |
| Author:
|
Kulosman, Hamid |
| Author:
|
Miller, Alica |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
137 |
| Issue:
|
1 |
| Year:
|
2012 |
| Pages:
|
99-111 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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:
|
13A15 |
| MSC:
|
13A99 |
| MSC:
|
13F20 |
| MSC:
|
37B05 |
| MSC:
|
54H20 |
| idZBL:
|
Zbl 1249.37001 |
| idMR:
|
MR2978448 |
| DOI:
|
10.21136/MB.2012.142790 |
| . |
| Date available:
|
2012-04-19T00:04:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/142790 |
| . |
| 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 |
| . |
