We study the set of star operations on local Noetherian domains D of dimension 1 such that the conductor (D: T ) (where T is the integral closure of D) is equal to the maximal ideal of D. We reduce this problem to the study of a class of closure operations (more precisely, multiplicative operations) in a finite extension k ⊆ B, where k is a field, and then we study how the cardinality of this set of closures vary as the size of k varies while the structure of B remains fixed.
Asymptotic for the number of star operations on one-dimensional noetherian domains
Spirito D.
2021-01-01
Abstract
We study the set of star operations on local Noetherian domains D of dimension 1 such that the conductor (D: T ) (where T is the integral closure of D) is equal to the maximal ideal of D. We reduce this problem to the study of a class of closure operations (more precisely, multiplicative operations) in a finite extension k ⊆ B, where k is a field, and then we study how the cardinality of this set of closures vary as the size of k varies while the structure of B remains fixed.File in questo prodotto:
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