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- W3006509201 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 $t^{c_0}S subseteq R$ for some integer $c_0 > 0$. 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 $M in mathrm {Max} R$, our result eventually shows that $mu _{R}(M) in {1,2,mu (H)}$ where $mu _{R}(M)$ (resp., $mu (H)$) stands for the minimal number of generators of $M$ (resp., $H$), which covers in the specific case the classical result of O. ForsterâR. G. Swan." @default.
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- W3006509201 date "2020-05-11" @default.
- W3006509201 modified "2023-10-18" @default.
- W3006509201 title "Efficient generation of ideals in core subalgebras of the polynomial ring $k[t]$ over a field $k$" @default.
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- W3006509201 doi "https://doi.org/10.1090/proc/15032" @default.
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