J. Korean Math. Soc. 2021; 58(5): 1239-1260
Online first article April 6, 2021 Printed September 1, 2021
https://doi.org/10.4134/JKMS.j200543
Copyright © The Korean Mathematical Society.
Dario Spirito
Universit\`a di Padova
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 $k\subseteq B$, 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
MSC numbers: 13A15, 13F10, 13G05, 13E10
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd