Positioned and primary positioned $\mathcal{C}$-semigroups

Carmelo Cisto; Raquel Tapia-Ramos

Paper

Positioned and primary positioned $\mathcal{C}$-semigroups

Abstract

Let

be a positive integer cone and

. A

-semigroup

-positioned if for every

we have that

belongs to

. In this work, we focus on this family of semigroups and introduce primary positioned

-semigroups, characterizing a subfamily of them through the perspective of irreducibility. Furthermore, we provide some procedures to compute all such semigroups, describing a family of graphs containing all the primary positioned

-semigroups for a fixed