A note on submonoids of N^k

Jerson Borja and Paola Castro – GJM, Volume 10, Issue 2 (2025), 21-27.

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décembre 27, 2025
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In this work, we show that for every nontrivial submonoid $H$ of $\mathbb N^k$ endowed with vector addition, the least positive integer $r$ for which $H$ is isomorphic to a submonoid of $\mathbb N^r$ coincides with the largest positive integer $t$ such that $H$ contains a free submonoid of rank $t$ . We also provide characterizations of when this least positive integer $r$ equals 1.

Categories: Issue2

Milestones:

Received: August 28, 2025
Accepted: December 09, 2025
Published: December 25, 2025

Authors:

Jerson Borja and Paola Castro
Departamento de Matemáticas y Estadística,
Universidad de Córdoba, Colombia.

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