%0 Journal Article 
%A Moreno Frías, María Ángeles
%A Nicola, J
%A Pardo Espino, Enrique
%A Thomas, H
%T Numerical semigroups that are not intersections of d-squashed semigroups
%D 2009
%@ 0008-4395
%U http://hdl.handle.net/10498/35327
%X We say that a numerical semigroup is d-squashed if it can be written in the form
S =1/N(a1, . . . , ad) ∩ Z
for N, a1, . . . , ad positive integers with gcd(a1, . . . , ad) = 1. Rosales and Urbano have shown that a
numerical semigroup is 2-squashed if and only if it is proportionally modular.
Recent works by Rosales et al. give a concrete example of a numerical semigroup that cannot
be written as an intersection of 2-squashed semigroups. We will show the existence of infinitely many
numerical semigroups that cannot be written as an intersection of 2-squashed semigroups. We also will
prove the same result for 3-squashed semigroups. We conjecture that there are numerical semigroups
that cannot be written as the intersection of d-squashed semigroups for any fixed d, and we prove some
partial results towards this conjecture.
%K Numerical Semigroups
%K d-squashed semigroups
%K proportionally modular numerical semigroup
%~ Universidad de Cádiz