On pseudo-Frobenius elements of submonoids of Nd

In this paper we study those submonoids of N d with a nontrivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension possible. We prove that these semigroups are a natural generalization of nume...

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Bibliographic Details
Published in:Collectanea mathematica (Barcelona) 2020, Vol.71 (1), p.189-204
Main Authors: García-García, J. I., Ojeda, I., Rosales, J. C., Vigneron-Tenorio, A.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
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Summary:In this paper we study those submonoids of N d with a nontrivial pseudo-Frobenius set. In the affine case, we prove that they are the affine semigroups whose associated algebra over a field has maximal projective dimension possible. We prove that these semigroups are a natural generalization of numerical semigroups and, consequently, most of their invariants can be generalized. In the last section we introduce a new family of submonoids of N d and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups.
ISSN:0010-0757
2038-4815
DOI:10.1007/s13348-019-00267-0