Let D be a domain with quotient field K. Let E K be a subset; the ring of D-integer-valued polynomials over E is Int(E;D) := ff 2 K[X]; f(E) Dg. The polynomial closure in D of a subset E K is the largest subset F K containing E such that Int(E;D) = Int(F;D), and it is denoted by clD(E). We study the polynomial closure of ideals in several classes of domains, including essential domains and domains of strong Krull-type, and we relate it with the t-closure. For domains of Krull-type we also compute the Krull dimension of Int(D).

Fontana, M., Izelgue, L., KABBAJ S., E., Tartarone, F. (1997). On the Krull dimension of domains of integer-valued polynomials. EXPOSITIONES MATHEMATICAE, 15, 433-465.

On the Krull dimension of domains of integer-valued polynomials

FONTANA, Marco;TARTARONE, FRANCESCA
1997-01-01

Abstract

Let D be a domain with quotient field K. Let E K be a subset; the ring of D-integer-valued polynomials over E is Int(E;D) := ff 2 K[X]; f(E) Dg. The polynomial closure in D of a subset E K is the largest subset F K containing E such that Int(E;D) = Int(F;D), and it is denoted by clD(E). We study the polynomial closure of ideals in several classes of domains, including essential domains and domains of strong Krull-type, and we relate it with the t-closure. For domains of Krull-type we also compute the Krull dimension of Int(D).
1997
Fontana, M., Izelgue, L., KABBAJ S., E., Tartarone, F. (1997). On the Krull dimension of domains of integer-valued polynomials. EXPOSITIONES MATHEMATICAE, 15, 433-465.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/115719
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