<abstract xmlns="http://www.w3.org/1999/xhtml">We give a characterization on the sets <italic>A</italic> ⊆ ℕ<italic>d</italic> such that the monoid generated by <italic>A</italic> is a generalized numerical semigroup (GNS) in ℕ<italic>d</italic>. Furthermore we give a procedure to compute the hole set ℕ<italic>d</italic> \ <italic>S</italic>, where <italic>S</italic> is a GNS, if a finite set of generators of <italic>S</italic> is known.</abstract>

We give a characterization on the sets A ⊆ ℕd such that the monoid generated by A is a generalized numerical semigroup (GNS) in ℕd. Furthermore we give a procedure to compute the hole set ℕd \ S, where S is a GNS, if a finite set of generators of S is known.

On the generators of a generalized numerical semigroup

Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra

Universitá Mediterranea di Reggio Calabria

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the generators of a generalized numerical semigroup"}

We give a characterization on the sets A ⊆ ℕd such that the monoid generated by A is a generalized numerical semigroup (GNS) in ℕd. Furthermore we give a...

On the generators of a generalized numerical semigroup

Published Online: Mar 02, 2019

Page range: 49 - 59

Received: Jan 27, 2018

Accepted: Apr 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0003

Keywords
Generalized numerical semigroup, minimal generators

© 2019 Carmelo Cisto et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the generators of a generalized numerical semigroup

Published Online: Mar 02, 2019

Page range: 49 - 59

Received: Jan 27, 2018

Accepted: Apr 27, 2018

DOI: https://doi.org/10.2478/auom-2019-0003

KeywordsGeneralized numerical semigroup, minimal generators

© 2019 Carmelo Cisto et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Generalized numerical semigroup, minimal generators