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

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 \(\geq 0\).


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)
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