On pseudo-Frobenius elements of submonoids of ℕ^d

2019/03/26 by García-García, J. I., Ojeda, I., Rosales, J. C. +1
#13D02 #20M14 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1903.11028

Abstract

In this paper we study those submonoids of 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 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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