A generalization of semiflows on monomials. (English) Zbl 1249.37001

Kulosman, Hamid; Miller, Alica

Math. Bohem. 137, No. 1, 99-111 (2012).

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 \(\geq 0\).

MSC:

37B05	Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
13A15	Ideals and multiplicative ideal theory in commutative rings
54H20	Topological dynamics (MSC2010)

Keywords:

monomial ideal; term ideal; Dickson’s lemma; semiflow