Turkish Journal of Mathematics
DOI
10.3906/mat-1708-16
Abstract
Let $n_1, n_2,\ldots, n_d$ be positive integers and $H $ be the numerical semigroup generated by $n_1,n_2, \ldots, n_d$. Let $A:=k[H]:=k[t^{n_1}, t^{n_2},\ldots, t^{n_d}]\cong k[x_1,x_2,\ldots,x_d]/I$ be the numerical semigroup ring of $H $ over $k.$ In this paper we give a condition $(*)$ that implies that the minimal number of generators of the defining ideal $I$ is bounded explicitly by its type. As a consequence for semigroups with $d=4$ satisfying the condition $(*)$ we have $\mu ({\rm in}(I))\leq 2(t(H))+1$.
Keywords
Frobenius number, pseudo-Frobenius number, almost Gorenstein ring, semigroup rings, monomial curve
First Page
2112
Last Page
2124
Recommended Citation
DUNG, NGUYEN THI
(2018)
"On the type and generators of monomial curves,"
Turkish Journal of Mathematics: Vol. 42:
No.
5, Article 4.
https://doi.org/10.3906/mat-1708-16
Available at:
https://journals.tubitak.gov.tr/math/vol42/iss5/4
