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http://dx.doi.org/10.4134/JKMS.j200543

ASYMPTOTIC FOR THE NUMBER OF STAR OPERATIONS ON ONE-DIMENSIONAL NOETHERIAN DOMAINS  

Spirito, Dario (Dipartimento di Matematica e Fisica Universita degli Studi "Roma Tre" and Dipartimento di Matematica Universita di Padova)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1239-1260 More about this Journal
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.
Keywords
Star operations; multiplicative operations; Noetherian domains;
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