The numerical semigroup of the integers which are bounded by a submonoid of N2

Autor:	Aureliano M. Robles-Pérez, José Carlos Rosales
Rok vydání:	2014
Předmět:	Combinatorics Set (abstract data type) Discrete mathematics Mathematics::Operator Algebras Applied Mathematics Numerical semigroup Bounded function Discrete Mathematics and Combinatorics Variety (universal algebra) Computer Science::Formal Languages and Automata Theory Mathematics
Zdroj:	Electronic Notes in Discrete Mathematics. 46:249-256
ISSN:	1571-0653
DOI:	10.1016/j.endm.2014.08.033
Popis:	Let M be a submonoid of ( N 2 , + ) such that the set A ( M ) = { n ∈ N | a n b for some ( a , b ) ∈ M } is non-empty. Then A ( M ) ∪ { 0 } is a numerical semigroup. We will show that a numerical semigroup S can be obtained in this way if and only if { a + b − 1 , a + b + 1 } ⊆ S for all a , b ∈ S \ { 0 } . We will see that such numerical semigroups form a Frobenius variety and we will study it.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::3a07238277987328664cff289a3a1c94 https://doi.org/10.1016/j.endm.2014.08.033 Zobrazit plný text záznamu Full Text from ScienceDirect