Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2020.09.24
  • Accepted : 2021.02.09
  • Published : 2021.09.01
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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.

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References

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