Efficient generation of ideals in core subalgebras of the polynomial ring k[t] over a field k

Naoki Endo, Shiro Goto, Naoyuki Matsuoka, Yuki Yamamoto

Research output: Contribution to journalArticlepeer-review

Abstract

This note aims at finding explicit and efficient generation of ideals in subalgebras R of the polynomial ring S = k[t] (k a field) such that tc0 S ⊆ R for some integer c0 > 0. The class of these subalgebras which we call cores of S includes the semigroup rings k[H] of numerical semigroups H, but much larger than the class of numerical semigroup rings. For R = k[H] and M ∈ Max R, our result eventually shows that μR(M) ∈ {1, 2, μ(H)} where μR(M) (resp., μ(H)) stands for the minimal number of generators of M (resp., H), which covers in the specific case the classical result of O. Forster-R. G. Swan.

Original languageEnglish
Pages (from-to)3283-3292
Number of pages10
JournalProceedings of the American Mathematical Society
Volume148
Issue number8
DOIs
Publication statusPublished - Aug 2020

Keywords

  • Integral closure of an ideal
  • Numerical semigroup ring
  • Rational closed point

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