A generalization of semiflows on monomials

Kulosman, Hamid ; Miller, Alica

Mathematica Bohemica, Tome 137 (2012) no. 1, pp. 99-111.

Résumé

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 $\geq 0$.

Détail

DOI : 10.21136/MB.2012.142790

Classification : 13A15, 13A99, 13F20, 37B05, 54H20
Keywords: monomial ideal; term ideal; Dickson's lemma; semiflow