2014/04/19 by Strazzanti, Francesco
#13H10 #20M14 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1404.4959
Let S,T be two numerical semigroups. We study when S is one half of T, with T almost symmetric. If we assume that the type of T, t(T), is odd, then for any S there exist infinitely many such T and we prove that 1 ≤ t(T) ≤ 2t(S)+1. On the other hand, if t(T) is even, there exists such T if and only if S is almost symmetric and different from ℕ; in this case the type of S is the number of even pseudo-Frobenius numbers of T. Moreover, we construct these families of semigroups using the numerical duplication with respect to a relative ideal.