Nullstellensatz and Skolem Properties for Integer-valued Polynomials
نویسنده
چکیده
Skolem and Nullstellensatz properties are analogues of the weak Nullstellensatz and Hilbert’s Nullstellensatz, respectively, for the ring of integervalued polynomials in several indeterminates Int(D) = {f ∈ K[x1, . . . , xn] | f(D) ⊆ D}, where D is a domain and K its quotient field. We show their equivalence when D is a Noetherian domain and extend the criterion of Brizolis and Chabert for Int(D) to have the Nullstellensatz property to all Noetherian domains D.
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