On the type and generators of monomial curves | Zendy

Nguyễn Thị Phương Dung | Zendy

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On the type and generators of monomial curves

Author(s) -

Nguyễn Thị Phương Dung

Publication year - 2018

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1708-16

Subject(s) - mathematics , semigroup , numerical semigroup , type (biology) , monomial , ideal (ethics) , combinatorics , bounded function , monomial ideal , generator (circuit theory) , discrete mathematics , polynomial ring , mathematical analysis , physics , polynomial , ecology , biology , philosophy , power (physics) , epistemology , quantum mechanics

Let n1, n2, . . . , nd be positive integers and H be the numerical semigroup generated by n1, n2, . . . , nd . Let A := k[H] := k[t1 , t2 , . . . , td ] ∼= k[x1, x2, . . . , xd]/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 μ(in(I)) ≤ 2(t(H)) + 1 .

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