A generalization of semiflows on monomials

Kulosman, Hamid, and Miller, Alica. "A generalization of semiflows on monomials." Mathematica Bohemica 137.1 (2012): 99-111. <http://eudml.org/doc/246358>.

@article{Kulosman2012,
abstract = {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 $\ge 0$.},
author = {Kulosman, Hamid, Miller, Alica},
journal = {Mathematica Bohemica},
keywords = {monomial ideal; term ideal; Dickson's lemma; semiflow; monomial ideal; term ideal; Dickson's lemma; semiflow},
language = {eng},
number = {1},
pages = {99-111},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A generalization of semiflows on monomials},
url = {http://eudml.org/doc/246358},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Kulosman, Hamid
AU - Miller, Alica
TI - A generalization of semiflows on monomials
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 1
SP - 99
EP - 111
AB - 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 $\ge 0$.
LA - eng
KW - monomial ideal; term ideal; Dickson's lemma; semiflow; monomial ideal; term ideal; Dickson's lemma; semiflow
UR - http://eudml.org/doc/246358
ER -