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arXiv · 1903.11028

On pseudo-Frobenius elements of submonoids of $\mathbb{N}^d$

J. I. García-García·I. Ojeda·J. C. Rosales·A. Vigneron-Tenorio
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Abstract

In this paper we study those submonoids of $\mathbb{N}^d$ which a non-trivial 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 $\mathbb{N}^d$ and using its pseudo-Frobenius elements we prove that the elements in the family are direct limits of affine semigroups.

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J. I. García-García, I. Ojeda, J. C. Rosales, A. Vigneron-Tenorio. 2019-03-26. On pseudo-Frobenius elements of submonoids of $\mathbb{N}^d$. https://arxiv.org/abs/1903.11028

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