Semigroup Forum

, Volume 97, Issue 3, pp 478–492 | Cite as

Frobenius restricted varieties in numerical semigroups

  • Aureliano M. Robles-Pérez
  • José Carlos Rosales
Research Article


The common behaviour of many families of numerical semigroups led to defining, firstly, the Frobenius varieties and, secondly, the (Frobenius) pseudo-varieties. However, some interesting families are still not covered by these definitions. To overcome this situation, here we introduce the concept of Frobenius restricted variety (or R-variety). We generalize most of the results for varieties and pseudo-varieties to R-varieties. In particular, we study the tree structure that arises within them.


R-varieties Frobenius restricted number Frobenius varieties Frobenius pseudo-varieties Monoids Numerical semigroups Tree (associated to an R-variety) 



The authors would like to thank both of the referees for providing constructive comments and help in improving the contents of this paper.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departamento de Matemática AplicadaUniversidad de GranadaGranadaSpain
  2. 2.Departamento de ÁlgebraUniversidad de GranadaGranadaSpain

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