Finitely Generated Submoduloids and Prime Submoduloids on a Nexus

Abstract

The concept of $\mathbb{N^{\infty}}$-submoduloid has been introduced in [5]. In this paper, the notions of a generating submoduloid, an additive absorption set, a prime $\mathbb{N^{\infty}}$-submoduloid, and an additive $\mathbb{N^{\infty}}$-submoduloid of an $\mathbb{N^{\infty}}$-moduloid are defined and some related results are investigated.