Let D be a domain, E a subset of its quotient field K, and Int(E,D) = {f ∈ K[X] | f (E) ⊆ D}. The polynomial closure of E is the set clD(E) = {x ∈ K | f (x) ∈ D, ∀ f ∈ Int(E,D)}.We compare the polynomial closure with the divisorial closure in a general setting and then in an essential domain. Especially,we showthat these two closures of ideals are the same if D is a Krull-type domain.
PARK M., H., Tartarone, F. (2005). Polynomial closure in Essential domains. MANUSCRIPTA MATHEMATICA, 117 n.1, 29-41 [10.1007/s00229-005-0547-4].
Polynomial closure in Essential domains
TARTARONE, FRANCESCA
2005-01-01
Abstract
Let D be a domain, E a subset of its quotient field K, and Int(E,D) = {f ∈ K[X] | f (E) ⊆ D}. The polynomial closure of E is the set clD(E) = {x ∈ K | f (x) ∈ D, ∀ f ∈ Int(E,D)}.We compare the polynomial closure with the divisorial closure in a general setting and then in an essential domain. Especially,we showthat these two closures of ideals are the same if D is a Krull-type domain.File in questo prodotto:
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