Frobenius restricted varieties in numerical semigroups

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...

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Bibliographic Details
Published inSemigroup forum Vol. 97; no. 3; pp. 478 - 492
Main Authors Robles-Pérez, Aureliano M., Rosales, José Carlos
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2018
Springer Nature B.V
Subjects
Algebra
Mathematics
Mathematics and Statistics
Research Article
Frobenius pseudo-varieties
Frobenius varieties
varieties
Numerical semigroups
Tree (associated to an
variety
Monoids
Frobenius restricted number
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Summary: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.
ISSN:0037-1912
1432-2137
DOI:10.1007/s00233-018-9949-y