Modular Frobenius pseudo-varieties

• Robles-Pérez, Aureliano M. ^[1] ; Rosales, José Carlos ^[1]
  1. [1] Universidad de Granada

     Universidad de Granada

     Granada, España

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 1, 2023, págs. 133-147
• Idioma: inglés
• DOI: 10.1007/s13348-021-00339-0
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• Resumen

  • If m∈N∖{0,1} and A is a finite subset of ⋃k∈N∖{0,1}{1,…,m−1}k, then we denote by C(m,A)={S∈Sm∣s1+⋯+sk−m∈S if (s1,…,sk)∈Sk and (s1modm,…,skmodm)∈A}.

    In this work we prove that C(m,A) is a Frobenius pseudo-variety. We also show algorithms that allows us to establish whether a numerical semigroup belongs to C(m,A) and to compute all the elements of C(m,A) with a fixed genus. Moreover, we introduce and study three families of numerical semigroups, called of second-level, thin and strong, and corresponding to C(m,A) when A={1,…,m−1}3, A={(1,1),…,(m−1,m−1)}, and A={1,…,m−1}2∖{(1,1),…,(m−1,m−1)}, respectively.