Let $\mathcal{C}\subseteq\mathbb{N}^p$ (for a non-zero natural number $p$) be a non-negative integer cone. A monoid $S \subseteq \mathcal{C}$ is called a $\mathcal{C}$-semigroup if its complement in the cone is finite. This structure naturally extends the classical notion of numerical semigroups, which are submonoids of the natural numbers with a finite complement in the set of natural numbers. This seminar invites the audience to explore the concept of $\mathcal{C}$-semigroup with the aim of generalize some properties of numerical semigroups from the perspective of some of their invariants. By combining theoretical results with computational examples, we gain a better understanding of these algebraic structures. This work, inspired by [1] is partially supported by the project ProyExcel_00868.

References. 

[1] J. Rosales, R. Tapia-Ramos, A. Vigneron-Tenorio. A computational approach to the study of finite-complement submonoids of an affine cone. arXiv:2409.06376